Prize policies: when applicable, a prize for the problem will be payed with a check in US dollars to the first person who sends me a complete solution which I will verify and recognize as correct.
ENTIRE FUNCTIONS:
ps pdf
An estimate of density of zeros. (Now
solved).
ps pdf Exceptional
set in Gross' Theorem.
ps pdf
Three problems on level sets of subharmonic functions arising in the
value distribution theory.
GEOMETRIC FUNCTION THEORY AND POTENTIAL THEORY:
ps pdf
Some constants studied by Littlewood (Updated Oct 2002).
ps pdf
"Hawaii Conjecture" (attributed to
Gauss).
ps pdf
Equilibrium points of Newtonian potentials (Maxwell)
ps pdf Does
every universe contain a place where you can stay at rest? (Lee Rubel)
$200
ps pdf Erdos'
problem on the length of lemniscates (at least $200).
Substantial recent progress is due to F. Nazarov and A. Fryntov.
DIFFERENTIAL EQUATIONS AND ITERATION IN THE COMPLEX DOMAIN:
ps pdf Meromorphic functions satisfying certain differential equations (E. Hille) Updated on May 22, 2007.
ps pdf
Wandering domains of entire functions.
ps pdf
Escaping sets for entire functions.
TRANSCENDENTAL HOLOMORPHIC CURVES:
ps pdf
Modified Cartan's Conjecture. $300
ps pdf Holomorphic curves with few inflection points. $500
RATIONAL FUNCTIONS AND RATIONAL CURVES:
ps pdf Rational
curves with real inflection points.
(B. and M. Shapiro, for more info, see
F. Sottile's page)
Now solved by Mukhin,
Tarasov and Varchenko.
When function theory became an
obsolete subject?
(Excerpt from a letter of Mittag-Leffler to Kowalevski.)
What is mathematics? Some expert's opinions.
jokes related to complex analysis
some problems, whose solutions I do know (level: undergraduate+)
stories about ODE, calculus and history