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Title:  Contributions to the Theory of QSeries and Mock Theta Functions 
Author(s):  Yesilyurt, Hamza 
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:  In Chapter 2, we prove, for the first time, a series of four related identities from Ramanujan's lost notebook. These are oneparameter identities which would directly imply some of the relations for the third order mock theta functions given by Ramanujan. In Chapter 3, we prove very general theorems on the periodicity of signs of the Taylor series coefficients of a large class of qproducts. S. Ramanujan, B. Richmond, G. Szekeres, G. E. Andrews, K. G. Ramanathan, M. D. Hirschhorn, and others have examined these types of qproducts with the goals of either producing asymptotic expansions or examining the periodicity of signs for their Taylor series coefficients. Further motivation arises from the fact that two of these products yield representations for the famous RogersRamanujan continued fraction and the RamanujanGollnitzGordon continued fraction. Our theorems greatly generalize the theorems of Andrews, Hirschhorn, and Ramanathan, and also have an application to another continued fraction of Ramanujan. An interesting representation for q;q10infinity is given in Chapter 4. This representation easily leads to a short proof of Ramanujan's famous congruence p(11n + 6) ≡ 0 (mod 11), where p(n) denotes the number of unrestricted partitions of the positive integer n. In the last chapter, we give simple elementary proofs, with methods known to Ramanujan, of several of Ramanujan's 40 identities for the RogersRamanujan functions. These identities have been previously proved by either L. J. Rogers, G. N. Watson, D. Bressoud, or A. J. F. Biagioli. However, it has not been realized by these authors that several of the identities are related. We also demonstrate how these ideas can be utilized to obtain new identities for the RogersRamanujan functions. 
Issue Date:  2004 
Type:  Text 
Language:  English 
Description:  99 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2004. 
URI:  http://hdl.handle.net/2142/86847 
Other Identifier(s):  (MiAaPQ)AAI3153471 
Date Available in IDEALS:  20150928 
Date Deposited:  2004 
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Dissertations and Theses  Mathematics

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