TY - JOUR

T1 - Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure

AU - Dixit, Atul

AU - Solynin, Alexander

PY - 2007/2

Y1 - 2007/2

N2 - We prove that for fixed u and v such that u, v ∈ [0, 1/2), the quotients θj (u|iπt)/θj (v|iπt), j = 1, 2, 3, 4, of the theta functions are monotone on 0 < t <∞. 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.

AB - We prove that for fixed u and v such that u, v ∈ [0, 1/2), the quotients θj (u|iπt)/θj (v|iπt), j = 1, 2, 3, 4, of the theta functions are monotone on 0 < t <∞. 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.

M3 - Article

SP - 1042

EP - 1053

JO - J. Math. Anal. Appl.

JF - J. Math. Anal. Appl.

ER -