1990
[1] T. D. Wooley, On simultaneous additive equations, III, Mathematika 37 (1990), no. 1, 85-96
1991
[2] T. D. Wooley, On simultaneous additive equations, I, Proc. London Math. Soc. (3) 63 (1991), no. 1, 1-34
[3] T. D. Wooley, On simultaneous additive equations, II, J. Reine Angew. Math. 419 (1991), 141-198
[4] R. C. Vaughan and T. D. Wooley, On a problem related to one of Littlewood and Offord, Quart. J. Math. Oxford (2) 42 (1991), no. 1, 379-386
[5] R. C. Vaughan and T. D. Wooley, Waring's problem: some refinements, Proc. London Math. Soc. (3) 63 (1991), no. 1, 35-68
1992
[6] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. (2) 135 (1992), no. 1, 131-164
[7] T. D. Wooley, On Vinogradov's mean value theorem, Mathematika 39 (1992), no. 2, 379-399
Corrigendum: ``On Vinogradov's mean value theorem'', Mathematika 40 (1993), no. 1, 152
1993
[8] T. D. Wooley, On Vinogradov's mean value theorem, II, Michigan Math. J. 40 (1993), no. 1, 681-686
[9] T. D. Wooley, A note on symmetric diagonal equations, Number Theory with an emphasis on the Markoff spectrum (Provo, UT, 1991), Editors: A. D. Pollington and W. Moran, Dekker, New York, 1993, pp 317-321
[10] T. D. Wooley, The application of a new mean value theorem to the fractional parts of polynomials, Acta Arith. 65 (1993), no. 2, 163-179
[11] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, III: eighth powers, Philos. Trans. Roy. Soc. London Ser. A 345 (1993), no. 1676, 385-396
1994
[12] T. D. Wooley, Quasi-diagonal behaviour in certain mean value theorems of additive number theory, J. Amer. Math. Soc. 7 (1994), 221-245
[13] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, II: sixth powers, Duke Math. J. 76 (1994), no. 3, 683-710
1995
[14] T. D. Wooley, New estimates for smooth Weyl sums, J. London Math. Soc. 51 (1995), 1--13.
[15] T. D. Wooley, New estimates for Weyl sums, Quart. J. Math. Oxford (2) 46 (1995), 119-127
[16] T. D. Wooley, Sums of two cubes, Internat. Math. Res. Notices (1995), 181-185
[17] C. M. Skinner and T. D. Wooley, Sums of two kth powers, J. Reine Angew. Math. 462 (1995), 57-68
[18] H. L. Montgomery, R. C. Vaughan and T. D. Wooley, Some remarks on Gauss sums associated with kth powers, Math. Proc. Cambridge Philos. Soc. 118 (1995), 21-33
[19] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, Acta Math. 174 (1995), no. 2, 147-240
[20] T. D. Wooley, Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour, Invent. Math. 122 (1995), no. 3, 421-451
[21] R. C. Vaughan and T. D. Wooley, On a certain nonary cubic form and related equations, Duke Math. J. 80 (1995), no. 3, 669-735
[22] R. C. Baker, J. Bruedern and T. D. Wooley, Cubic diophantine inequalities, Mathematika 42 (1995), 264-277
1996
[23] T. D. Wooley, An affine slicing approach to certain paucity problems, Analytic Number Theory: Proceedings of a Conference in Honor of Heini Halberstam (B. C. Berndt, H. G. Diamond and A. J. Hildebrand, eds.), vol. 2, 1996, pp. 803-815, Prog. Math. 139, Birkhauser, Boston.
[24] T. D. Wooley, A note on simultaneous congruences, J. Number Theory 58 (1996), 288-297
[25] T. D. Wooley, Some remarks on Vinogradov's mean value theorem and Tarry's problem, Monatsh. Math. 122 (1996), 265-273
1997
[26] R. C. Vaughan and T. D. Wooley, A special case of Vinogradov's mean value theorem, Acta Arith. 79 (1997), no. 3, 193-204
[27] C. M. Skinner and T. D. Wooley, On the paucity of non-diagonal solutions in certain diagonal Diophantine systems, Quart. J. Math. Oxford (2) 48 (1997), no. 2, 255-277
[28] T. D. Wooley, On exponential sums over smooth numbers, J. Reine Angew. Math. 488 (1997), 79-140
[29] T. D. Wooley, Linear spaces on cubic hypersurfaces, and pairs of cubic homogeneous equations, Bull. London Math. Soc. 29 (1997), 556-562
[30] T. D. Wooley, Forms in many variables, Analytic Number Theory: Proceedings of the 39th Taniguchi International Symposium, Kyoto, May 1996 (Y. Motohashi, ed.), London Mathematical Society Lecture Notes 247, Cambridge University Press, Cambridge, 1997, pp. 361-376
1998
[31] M. A. Bennett, N. P. Dummigan and T. D. Wooley, The representation of integers by binary additive forms, Compositio Math. 111 (1998), 15-33
[32] T. D. Wooley, On the local solubility of diophantine systems, Compositio Math. 111 (1998), 149-165
[33] R. C. Vaughan and T. D. Wooley, On the distribution of generating functions, Bull. London Math. Soc. 30 (1998), 113-122
[34] J. Bruedern and T. D. Wooley, The addition of binary cubic forms, Philos. Trans. Roy. Soc. London Ser. A 356 (1998), 701-737
[35] J. Bruedern, A. Granville, A. Perelli, R. C. Vaughan and T. D. Wooley, On the exponential sum over k-free numbers, Philos. Trans. Roy. Soc. London Ser. A 356 (1998), 739-761
[36] A. Balog and T. D. Wooley, On strings of consecutive integers with no large prime factors, J. Austral. Math. Soc. Ser. A 64 (1998), 266-276
[37] T. D. Wooley, An explicit version of Birch's Theorem, Acta Arith. 85 (1998), 79-96
[38] M. Kuehleitner, W. G. Nowak, J. Schoissengeier and T. Wooley, On sums of two cubes: an $\Omega_+$-estimate for the error term, Acta Arith. 85 (1998), 179-195
[39] K. Kawada and T. D. Wooley, Sums of fifth powers and related topics, Acta Arith. 87 (1998), 27-65
[40] T. D. Wooley, On simultaneous additive equations, IV, Mathematika 45 (1998), 319-335
1999
[41] W. Y. Tsui and T. D. Wooley, The paucity problem for simultaneous quadratic and biquadratic equations, Math. Proc. Cambridge Philos. Soc. 126 (1999), no. 2, 209-221.
[42] T. D. Wooley, Diophantine problems in many variables: the role of additive number theory, S. D. Ahlgren et al. (eds.), Topics in Number Theory, Kluwer Academic Publishers, 1999, pp. 49-83.
[43] K. Kawada and T. D. Wooley, Sums of fourth powers and related topics, J. Reine Angew. Math. 512 (1999), 173-223.
[44] J. Bruedern and T. D. Wooley, On Waring's problem: a square, four cubes and a biquadrate, Math. Proc. Cambridge Philos. Soc. 127 (1999), 193-200.
[45] T. D. Wooley, On Weyl's inequality, Hua's Lemma, and exponential sums over binary forms, Duke Math. J. 100 (1999), 373-423.
[46] A. Balog, J. Bruedern and T. D. Wooley, On smooth gaps between consecutive prime numbers, Mathematika 46 (1999), 57-75.
2000
[47] T. D. Wooley, Sums and differences of two cubic polynomials, Monatsh. Math. 129 (2000), no. 2, 159-169.
[48] J. Bruedern, A. Perelli and T. D. Wooley, Twins of k-free numbers and their exponential sum, Michigan Math. J. 47 (2000), 173-190.
[49] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's Problem, IV: higher powers, Acta Arith. 94 (2000), no. 3, 203-285.
[50] T. D. Wooley, Quasi-diagonal behaviour and smooth Weyl sums, Monatsh. Math. 130 (2000), 161-170.
[51] A. Balog and T. D. Wooley, Sums of two squares in short intervals, Canad. J. Math. 52 (2000), 673-694.
[52] T. D. Wooley, Weyl's inequality and exponential sums over binary forms, Funct. Approx. Comment. Math. 28 (2000), 83--95.
[53] J. Bruedern and T. D. Wooley, On Waring's problem: two cubes and seven biquadrates, Tsukuba J. Math. 24 (2000), no. 2, 387--417.
[54] T. D. Wooley, Sums of three cubes, Mathematika 47 (2000), no. 1-2, 53--61.
[55] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, II: the binary Goldbach problem, Mathematika 47 (2000), no. 1-2, 117--125.
2001
[56] J. Bruedern and T. D. Wooley, On Waring's problem for cubes and smooth Weyl sums, Proc. London Math. Soc. (3) 82 (2001), no. 1, 89--109.
[57] K. Kawada and T. D. Wooley, On the Waring-Goldbach problem for fourth and fifth powers, Proc. London Math. Soc. (3) 83 (2001), 1--50.
[58] M. B. S. Laporta and T. D. Wooley, The representation of almost all numbers as sums of unlike powers, J. Theor. Nombres Bordeaux 13 (2001), 227--240.
[59] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, I: Waring's problem for cubes, Ann. Sci. Ecole Norm. Sup. (4) 34 (2001), 471--501.
[60] J. Bruedern and T. D. Wooley, On Waring's problem: three cubes and a sixth power, Nagoya Math. J. 163 (2001), 13--53.
[61] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, III: asymptotic formulae, Acta Arith. 100 (2001), no. 3, 267--289.
[62] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, IV: lower bound methods, Quart. J. Math. Oxford (2) 52 (2001), 423--436.
[63] T. D. Wooley, Hua's lemma and exponential sums over binary forms, in: "Rational points on algebraic varieties", Progr. Math., vol. 199, Birkhauser, Boston, Boston, MA, 2001, pp. 405--446.
2002
[64] S. T. Parsell and T. D. Wooley, On pairs of diagonal quintic forms, Compositio Math. 131 (2002), 61--96.
[65] T. D. Wooley, Slim exceptional sets for sums of cubes, Canad. J. Math. 54 (2002), 417--448.
[66] T. D. Wooley, Slim exceptional sets in Waring's problem: one square and five cubes, Quart. J. Math. 53 (2002), 111--118.
[67] T. D. Wooley, Slim exceptional sets for sums of four squares, Proc. London Math. Soc. (3) 85 (2002), 1--21.
[68] K. Kawada and T. D. Wooley, Slim exceptional sets for sums of fourth and fifth powers, Acta Arith. 103 (2002), 225--248.
[69] J. Bruedern and T. D. Wooley, Hua's lemma and simultaneous diagonal equations, Bull. London Math. Soc. 34 (2002), 279--283.
[70] T. D. Wooley, Diophantine methods for exponential sums, and exponential sums for diophantine problems, Proceedings of the International Congress of Mathematicians, August 20--28, 2002, Beijing, Volume II, Higher Education Press, 2002, pp. 207--217.
[71] R. C. Vaughan and T. D. Wooley, Waring's problem: a survey, in: Number Theory for the Millenium, Vol. III (Bennett et al., eds.), A. K. Peters, 2002, pp. 301--340.
[72] S. T. Parsell and T. D. Wooley, A quasi-paucity problem, Michigan Math. J. 50 (2002), no. 3, 461--469.
[73] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VI: representing primes, and related problems, Glasg. Math. J. 44 (2002), 419--434.
2003
[74] T. D. Wooley, On the difficulty of the local solubility problem for additive equations, Acta Arith. 107 (2003), 127--156.
[75] J. Bruedern and T. D. Wooley, The paucity problem for certain pairs of diagonal equations, Quart. J. Math. 54 (2003), 41--48.
[76] T. D. Wooley, Slim exceptional sets and the asymptotic formula in Waring's problem, Math. Proc. Cambridge Philos. Soc. 134 (2003), 193--206.
[77] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, V: mixed problems of Waring's type, Math. Scand. 92 (2003), 181--209.
[78] R. Dietmann and T. D. Wooley, Pairs of cubic forms in many variables, Acta Arith 110 (2003), 125--140.
[79] T. D. Wooley, On Vu's thin basis theorem in Waring's problem, Duke Math. J. 120 (2003), 1--34.
[80] T. D. Wooley, On Diophantine inequalities: Freeman's asymptotic formulae, Proceedings of the Session in analytic number theory and Diophantine equations (Bonn, January -- June, 2002), Bonn 2003, Edited by D. R. Heath-Brown and B. Z. Moroz, Bonner Mathematische Schriften, Nr. 360, Article 30, 32pp.
2004
[81] T. D. Wooley, A light-weight version of Waring's problem, J. Austral. Math. Soc. 76 (2004), 303--316.
[82] J. Bruedern and T. D. Wooley, Asymptotic formulae for pairs of diagonal equations, Math. Proc. Cambridge Philos. Soc. 137 (2004), 227--235.
[83] Jianya Liu, T. D. Wooley and Gang Yu, The quadratic Waring-Goldbach problem, J. Number Theory 107 (2004), 298--321.
[84] J. Bruedern and T. D. Wooley, Additive representation in short intervals, I: Waring's problem for cubes, Compositio Math. 140 (2004), 1197--1220.
2005
[85] J.-M. Deshouillers, K. Kawada and T. D. Wooley, On sums of sixteen biquadrates, Mem. Soc. Math. Fr. (N.S.) No. 100 (2005), vi+120pp.
2007
[86] J. Bruedern and T. D. Wooley, The density of integral solutions for pairs of diagonal cubic equations, Clay Math. Proceedings 7 (2007), 57--76.
[87] Yu-Ru Liu and T. D. Wooley, The unrestricted variant of Waring's problem in function fields, Funct. Approx. Comment. Math. 37 (2007), 285--292.
[88] J. Bruedern and T. D. Wooley, The Hasse principle for pairs of diagonal cubic forms, Annals of Math. (2) 166 (2007), no. 3, 865--895.
2008
[89] T. D. Wooley, Artin's Conjecture for septic and unidecic forms, Acta Arith. 133 (2008), 25--35.
[90] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VII: restricted moments of the number of representations, Tsukuba J. Math. 32 (2008), 383--406.
2009
[91] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VIII: Diophantine inequalities in review, Number Theory. Dreaming in Dreams, Proceedings of the 5th China-Japan Seminar, Higashi-Osaka, Japan, 27-31 August 2008, eds. T. Aoki, S. Kanemitsu and J. Y. Liu, World Scientific, 2009, pp. 20--79.
2010
[92] J. Bruedern, R. Dietmann, J. Y. Liu and T. D. Wooley, A Birch-Goldbach theorem, Arch. Math. (Basel) 94 (2010), 53--58.
[93] Yu-Ru Liu and T. D. Wooley, Waring's problem in function fields, J. Reine Angew. Math. 638 (2010), 1--67.
[94] T. D. Wooley, A note on simultaneous congruences, II: Mordell revised, J. Austral Math. Soc. 88 (2010), 261--275.
[95] K. Kawada and T. D. Wooley, Davenport's method and slim exceptional sets: the asymptotic formulae in Waring's problem, Mathematika 56 (2010), no. 2, 305--321.
[96] P. Salberger and T. D. Wooley, Rational points on complete intersections of higher degree, and mean values of Weyl sums, J. London Math. Soc. (2) 82 (2010), no. 2, 317--342.
[97] K. Kawada and T. D. Wooley, Relations between exceptional sets for additive problems, J. London Math. Soc. (2) 82 (2010), no. 2, 437--458.
[98] J. Bruedern and T. D. Wooley, The asymptotic formulae in Waring's problem for cubes, J. Reine Angew. Math. 647 (2010), 1--23.
[99] J. Bruedern and T. D. Wooley, On Waring's problem: three cubes and a minicube, Nagoya Math. J. 200 (2010), 59--91.
2011
[100] J. Bruedern and T. D. Wooley, Asymptotic formulae for pairs of diagonal cubic equations, Canad. J. Math. 63 (2011), 38--54.
[101] J. Bruedern and T. D. Wooley, Sparse variance for primes in arithmetic progression, Quart. J. Math. 62 (2011), 289--305.
[102] Y. Dodis, X. Li, T. D. Wooley and D. Zuckerman, Privacy amplification and non-malleable extractors via character sums, Proceedings of the 52nd Annual IEEE Symposium on Foundations of Computer Science (FOCS 2011), 668--677.
2012
[103] K. D. Boklan and T. D. Wooley, On Weyl sums for smaller exponents, Funct. Approx. Comment. Math. 46 (2012), 91--107.
[104] T. D. Wooley, The asymptotic formula in Waring's problem, Internat. Math. Res. Notices (2012), no. 7, 1485--1504.
Corrigendum: "The asymptotic formula in Waring's problem", Internat. Math. Res. Notices (2015), no. 20, 10702.
[105] T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, Ann. of Math. (2) 175 (2012), no. 3, 1575--1627.
[106] C. V. Spencer and T. D. Wooley, Diophantine inequalities and quasi-algebraically closed fields, Israel J. Math. 191 (2012), 721--738.
[107] T. D. Wooley and T. D. Ziegler, Multiple recurrence and convergence along the primes, Amer. J. Math. 134 (2012), 1705--1732.
2013
[108] T. D. Wooley, Vinogradov's mean value theorem via efficient congruencing, II, Duke Math. J. 162 (2013), 673--730.
[91v2] J. Bruedern, K. Kawada and T. D. Wooley, Additive representation in thin sequences, VIII: Diophantine inequalities in review, Number Theory: Arithmetic in Shangri-La, Proceedings of the 6th China-Japan Seminar, Shanghai, China 15-17 August 2011, eds. S. Kanemitsu, et al., World Scientific, Singapore, 2013, pp. 17--76. (Reprint of [91] with corrections to equation numbers).
[109] J. Bruedern, K. Kawada and T. D. Wooley, Annexe to the gallery: an addendum to "Additive representation in thin sequences, VIII: Diophantine inequalities in review", Number Theory: Arithmetic in Shangri-La, Proceedings of the 6th China-Japan Seminar, Shanghai, China 15-17 August 2011, eds. S. Kanemitsu, et al., World Scientific, Singapore, 2013, pp. 77--82
[110] S. T. Parsell, S. M. Prendiville and T. D. Wooley, Near-optimal mean value estimates for multidimensional Weyl sums, Geom. Funct. Anal. 23 (2013), 1962--2024.
[111] T. D. Wooley, On Waring's problem: some consequences of Golubeva's method, J. London Math. Soc. (2) 88 (2013), no. 3, 699--715.
2014
[112] J. B. Friedlander and T. D. Wooley, On Waring's problem: two squares and three biquadrates, Mathematika 60 (2014), no. 1, 153--165.
[113] T. D. Wooley, On Waring's problem: two squares, two cubes and two sixth powers, Quart J. Math. 65 (2014), no. 1, 305--317.
[114] Y. Dodis, X. Li, T. D. Wooley and D. Zuckerman, Privacy amplification and non-malleable extractors via character sums, SIAM J. Comput. 43 (2014), no. 2, 800--830.
[115] S. T. Parsell and T. D. Wooley, Exceptional sets for Diophantine inequalities, Internat. Math. Res. Notices (2014), no. 14, 3919--3974.
[116] T. D. Wooley, Translation invariance, exponential sums, and Waring's problem, Proceedings of the International Congress of Mathematicians, August 13--21, 2014, Seoul, Korea, Volume II, Kyung Moon Sa Co. Ltd., Seoul, Korea, 2014, pp. 505--529.
[117] T. D. Wooley, On Linnik's conjecture: sums of squares and microsquares, Internat. Math. Res. Notices (2014), no. 20, 5713--5736.
[118] J. Bruedern and T. D. Wooley, Subconvexity for additive equations: pairs of undenary cubic forms, J. Reine Angew. Math. 696 (2014), 31--67.
[119] K. Ford and T. D. Wooley, On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing, Acta Math. 213 (2014), no. 2, 199--236.
2015
[120] T. D. Wooley, Rational solutions of pairs of diagonal equations, one cubic and one quadratic, Proc. London Math. Soc. (3) 110 (2015), no. 2, 325--356.
[121] T. D. Wooley, Artin's Conjecture and systems of diagonal equations, Forum Math. 27 (2015), no. 4, 2259--2265; arxiv:1307.1396, https://doi.org/10.1515/forum-2013-0109.
[122] T. D. Wooley, Sums of three cubes, II, Acta Arith. 170 (2015), no. 1, 73--100.
[123] T. D. Wooley, Multigrade efficient congruencing and Vinogradov's mean value theorem, Proc. London Math. Soc. (3) 111 (2015), no. 3, 519--560; arxiv:1310.8447, doi.org/10.1112/plms/pdv034.
[124] J. Bruedern and T. D. Wooley, Cubic moments of Fourier coefficients and pairs of diagonal quartic forms, J. Eur. Math. Soc. 17 (2015), no. 11, 2887--2901.
[125] B. Wei and T. D. Wooley, On sums of powers of almost equal primes, Proc. London Math. Soc. (3) 111 (2015), no. 5, 1130--1162.
[126] T. D. Wooley, Mean value estimates for odd cubic Weyl sums, Bull. London Math. Soc. 47 (2015), no. 6, 946--957; arxiv:1401.7152, doi.org/10.1112/blms/bdv066.
2016
[127] J. Bruedern and T. D. Wooley, The Hasse principle for systems of diagonal cubic forms, Math. Ann. 364 (2016), no. 3-4, 1255--1274.
Correction to: "The Hasse principle for systems of diagonal cubic forms", Math. Ann. 389 (2024), no. 1, 997--998; https://doi.org/10.1007/s00208-023-02645-3.
[128] T. D. Wooley, The cubic case of the main conjecture in Vinogradov's mean value theorem, Adv. Math. 294 (2016), 532--561; arxiv:1401.3150, https://doi.org/10.1016/j.aim.2016.02.033.
[129] T. D. Wooley, Perturbations of Weyl sums, Internat. Math. Res. Notices 2016 (2016), no. 9, 2632--2646.
[130] T. D. Wooley, Solvable points on smooth projective varieties, Monatsh. Math. 180 (2016), no. 2, 391--403.
[131] A. V. Kumchev and T. D. Wooley, On the Waring-Goldbach problem for eighth and higher powers, J. London Math. Soc. (2) 93 (2016), no. 3, 811--824; arxiv:1510.00982.
[132] J. Bruedern and T. D. Wooley, Correlation estimates for sums of three cubes, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), no. 3, 789--816; arXiv:1404.3846, doi:10.2422/2036-2145.201409_013.
[133] T. D. Wooley, On Waring's problem for intermediate powers, Acta Arith. 176 (2016), no. 3, 241--247; arXiv:1602.03221, doi:10.4064/aa8439-8-2016.
2017
[134] T. D. Wooley, Approximating the main conjecture in Vinogradov's mean value theorem, Mathematika 63 (2017), no. 1, 292--350; arXiv:1401.2932, doi:10.1112/S0025579316000279.
[135] T. D. Wooley, Discrete Fourier restriction via efficient congruencing, Internat. Math. Res. Notices 2017 (2017), no. 5, 1342--1389; arXiv:1508.05329, doi:10.1093/imrn/rnw031.
[136] A. Balog and T. D. Wooley, A low-energy decomposition theorem, Quart. J. Math. 68 (2017), no. 1, 207--226; arXiv:1510.03309, doi:10.1093/qmath/haw023.
[137] T. D. Wooley, A superpowered Euclidean prime generator, Amer. Math. Monthly 124 (2017), no. 4, 351--352; arXiv:1607.05267, doi:10.4169/amer.math.monthly.124.4.351.
[138] A. V. Kumchev and T. D. Wooley, On the Waring-Goldbach problem for seventh and higher powers, Monatsh. Math. 183 (2017), no. 2, 303--310; arXiv:1602.08592, doi:10.1007/s00605-016-0936-7.
[139] J. Bruedern and T. D. Wooley, Additive representation in short intervals, II: sums of two like powers, Math. Z. 286 (2017), no. 1-2, 179--196; arXiv:1506.01902, doi:10.1007/s00209-016-1759-x.
[140] J. Brandes and T. D. Wooley, Vinogradov systems with a slice off, Mathematika 63 (2017), no. 3, 797--817; arXiv:1707.06047, doi:10.1112/S0025579317000134.
2018
[141] R. C. Vaughan and T. D. Wooley, The asymptotic formula in Waring's problem: higher order expansions, J. Reine Angew. Math. 742 (2018), 17--46; arxiv:1309.0443, doi:10.1515/crelle-2015-0098.
[142] J. Bruedern and T. D. Wooley, Arithmetic harmonic analysis for smooth quartic Weyl sums: three additive equations, J. Eur. Math. Soc. 20 (2018), no. 10, 2333--2356; arxiv:1507.07465, doi:10.4171/JEMS/813.
2019
[143] T. D. Wooley, Nested efficient congruencing and relatives of Vinogradov's mean value theorem, Proc. London Math. Soc. (3) 118 (2019), no. 4, 942--1016; arxiv:1708.01220, doi.org/10.1112/plms.12204.
[144] J. Bruedern and T. D. Wooley, An instance where the major and minor arc integrals meet, Bull. London Math. Soc. 51 (2019), no. 6, 1113--1128; arxiv:1902.05155, doi.org/10.1112/blms.12291.
2020
[145] J. W. Bober, D. Fretwell, G. Martin and T. D. Wooley, Smooth values of polynomials, J. Austral. Math. Soc. 108 (2020), no. 2, 245--261; arxiv:1710.01970, doi:10.1017/S1446788718000320.
2021
[146] J. Brandes and T. D. Wooley, Optimal mean value estimates beyond Vinogradov's mean value theorem, Acta Arith. 200 (2021), no. 2, 149--182; arxiv:1901.03153, doi:10.4064/aa200824-9-3.
2022
[147] J. Bruedern and T. D. Wooley, On smooth Weyl sums over biquadrates and Waring's problem, Acta Arith. 204 (2022), no. 1, 19--40; arxiv:2110.04348, doi:10.4064/aa210910-6-4.
[148] J. Bruedern and T. D. Wooley, A paucity problem for certain triples of diagonal equations, Bull. London Math. Soc. 54 (2022), no. 4, 1396--1412; arxiv:2106.03986, doi.org/10.1112/blms.12636.
[149] K. Hughes and T. D. Wooley, Discrete restriction for (x,x^3) and related topics, Internat. Math. Res. Notices 2022 (2022), no. 20, 15612--15631; arxiv:1911.12262, doi.org/10.1093/imrn/rnab113.
2023
[150] W. Heap, A. Sahay and T. D. Wooley, A paucity problem associated with a shifted integer analogue of the divisor function, J. Number Theory 242 (2023), 660--668; arxiv:2108.00287, doi.org/10.1016/j.jnt.2022.05.006.
[151] T. D. Wooley, Subconvexity in the inhomogeneous cubic Vinogradov system, J. London Math. Soc. 107 (2023), no. 2, 798--817; arxiv:2202.05804, doi.org/10.1112/jlms.12698.
[152] J. Bruedern and T. D. Wooley, Pairs of diagonal quartic forms: the non-singular Hasse principle, Quart. J. Math. 74 (2023), no. 1, 101--128; arxiv:2110.04349, doi.org/10.1093/qmath/haac019.
[153] T. D. Wooley, Subconvexity in inhomogeneous Vinogradov systems, Quart. J. Math. 74 (2023), no. 1, 389--418; arxiv:2202.14003, doi.org/10.1093/qmath/haac027.
[154] T. D. Wooley, Finite abelian groups via congruences, Amer. Math. Monthly 130 (2023), no. 5, 482--484; arxiv:2211.10520, doi.org/10.1080/00029890.2023.2178221.
[155] T. D. Wooley, The paucity problem for certain symmetric Diophantine equations, Bull. Austral. Math. Soc. 108 (2023), no. 1, 29--39; arxiv:2211.10500, doi.org/10.1017/S000497272200096X.
[156] T. D. Wooley, Paucity problems and some relatives of Vinogradov's mean value theorem, Math. Proc. Cambridge Philos Soc. 175 (2023), no. 2, 327--343; arxiv:2107.12238, doi.org/10.1017/S0305004123000166.
[157] J. Bruedern and T. D. Wooley, Pairs of diagonal quartic forms: the asymptotic formulae, Internat. Math. Res. Notices 2023 (2023), no. 18, 15928--15975; arxiv:2211.10397, doi.org/10.1093/imrn/rnad021.
[158] J. Bruedern and T. D. Wooley, On Waring's problem for larger powers, J. Reine Angew. Math. 805 (2023), 115--142; arxiv:2211.10380, doi.org/10.1515/crelle-2023-0072.
2024
[159] J. Bruedern and T. D. Wooley, On Waring's problem: beyond Freiman's theorem, J. London Math. Soc. 109 (2024), no. 1, Paper No. e12820, 25pp.; arxiv:2302.12920, doi.org/10.1112/jlms.12820.
[160] T. D. Wooley, Rational lines on diagonal hypersurfaces and subconvexity via the circle method, Trans. Amer. Math. Soc. 377 (2024), no. 3, 2125--2147; arxiv:2305.05071, doi.org/10.1090/tran/9077.
Accepted
[161] T. D. Wooley, Condensations and densifications for sets of large diameter, accepted, to appear in Combinatorial and Additive Number Theory VI -- CANT, New York, USA, 2022 and 2023, Ed. Melvyn B. Nathanson, Springer Proceedings in Mathematics and Statistics, 45pp.; arXiv:2305.19968.
[162] J. Bruedern and T. D. Wooley, Partitio Numerorum: sums of squares and higher powers, accepted, to appear in Funct. Approx. Comment. Math., 44pp.; arXiv:2402.09537.
Submitted
[163] T. D. Wooley, Subconvexity and the Hilbert-Kamke problem, submitted, 13pp; arXiv:2201.02699.
[164] J. Bruedern and T. D. Wooley, Partitio Numerorum: sums of a prime and a number of k-th powers, submitted, 26pp; arXiv:2211.10387.
[165] T. H. Le, Y.-R. Liu and T. D. Wooley, Equidistribution of polynomial sequences in function fields, with applications, submitted, 37pp; arXiv:1311.0892v2.
[166] J. W. Bober, L. Du, D. Fretwell, G. S. Kopp and T. D. Wooley, On 2-superirreducible polynomials over finite fields, submitted, 10pp; arXiv:2309.15304.
Useful notes
[a] T. D. Wooley, An elementary discrete inequality, 2pp.