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Title:Infinite Series Identities in the Theory of Elliptic Functions and Q-Series
Author(s):Kongsiriwong, Sarachai
Doctoral Committee Chair(s):Berndt, Bruce C.
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Abstract:We prove several infinite series identities. In Chapter 2, We extend C. L. Siegel's method of proving the Dedekind-eta function transformation by integrating some selected functions over a positively oriented polygon, generalizing Siegel's integration over a parallelogram. As consequences, we obtain a generalization of the Dedekind-eta function transformation and generalizations of other transformation formulas. In Chapter 3, we adapt B. C. Berndt and A. Zaharescu's method to establish a multi-variable theta product identity of a function of k + 1 complex variables. In Chapter 4, we give a simple new proof of the classical theta-function inversion formula. In Chapter 5, we give two general methods for proving q-series-product identities. The first method uses basic properties of roots of unity. The second method generalizes S. Bhragava's argument proving the quintuple product identity. By comparing the results from the two methods, we obtain new identities. Using these identities, we can derive certain modular equations. In Chapter 6, we evaluate certain infinite series involving hyperbolic functions by using the cubic theory of elliptic functions.
Issue Date:2003
Description:128 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003.
Other Identifier(s):(MiAaPQ)AAI3111562
Date Available in IDEALS:2015-09-28
Date Deposited:2003

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