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Title:  Infinite Series Identities in the Theory of Elliptic Functions and QSeries 
Author(s):  Kongsiriwong, Sarachai 
Doctoral Committee Chair(s):  Berndt, Bruce C. 
Department / Program:  Mathematics 
Discipline:  Mathematics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Mathematics 
Abstract:  We prove several infinite series identities. In Chapter 2, We extend C. L. Siegel's method of proving the Dedekindeta 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 Dedekindeta function transformation and generalizations of other transformation formulas. In Chapter 3, we adapt B. C. Berndt and A. Zaharescu's method to establish a multivariable theta product identity of a function of k + 1 complex variables. In Chapter 4, we give a simple new proof of the classical thetafunction inversion formula. In Chapter 5, we give two general methods for proving qseriesproduct 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 
Type:  Text 
Language:  English 
Description:  128 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2003. 
URI:  http://hdl.handle.net/2142/86827 
Other Identifier(s):  (MiAaPQ)AAI3111562 
Date Available in IDEALS:  20150928 
Date Deposited:  2003 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois