Ramanujan's identities and monotonicity properties of quotients of theta functions

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Title: Ramanujan's identities and monotonicity properties of quotients of theta functions
Author: Dixit, Atul Abhay
Abstract: In this work , we prove monotonicity results associated with certain quotients of theta functions . The monotonicity result for the second theta function has its application in the extremal problems on harmonic measure and steady -state heat distributions in special configurations . Along with these results , we include the generalization of theta functions in signature 3 and illustrate a beautiful identity of Ramanujan associated with the inversion of an analogue of an elliptic integral in signature 3 .
URI: http : / /hdl .handle .net /2346 /13534
Date: 2006-08

Citation

Ramanujan's identities and monotonicity properties of quotients of theta functions. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /13534 .

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