Monotonicity of quotients of theta functions related to an extremal problem on harmonic measure |
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| Authors: | Atul Dixit |
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| Institution: | Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, TX 79409, USA |
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| Abstract: | 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. |
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| Keywords: | Jacobi theta function Weierstrass &weierp -function Monotonicity Harmonic measure |
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