TY - JOUR

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

AU - Dixit, Atul

AU - Solynin, Alexander Yu

N1 - Funding Information:
* Corresponding author. Current address: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA. E-mail address: atuladixit@rediffmail.com (A. Dixit). 1 Supported in part by the NSF grant DMS-0412908.

PY - 2007/12/15

Y1 - 2007/12/15

N2 - We prove that for fixed u and v such that u, v ∈ [0, 1 / 2), the quotients θj (u | i π t) / θj (v | i π t), 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 | i π t) / θj (v | i π t), 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.

KW - Harmonic measure

KW - Jacobi theta function

KW - Monotonicity

KW - Weierstrass ℘-function

UR - http://www.scopus.com/inward/record.url?scp=34548098985&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2007.03.041

DO - 10.1016/j.jmaa.2007.03.041

M3 - Article

AN - SCOPUS:34548098985

SN - 0022-247X

VL - 336

SP - 1042

EP - 1053

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -