Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure

[摘要] We prove that for fixed u and v such that u, v is an element of [0, 1/2), the quotients theta(j)(u vertical bar i pi t)/theta(j) (v vertical bar i pi t), j = 1, 2, 3, 4, of the theta functions are monotone on 0 < t < infinity. The case v = 0 has been used by the second author to study a generalization of Gonchar's problem on harmonic measure of radial slits. Published by Elsevier Inc.

[发布日期] 2007-12-15

[关键词] jacobi theta function;weierstrass p-function;monotonicity;harmonic measure