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Title:  The Construction and Applications of Modular Equations 
Author(s):  Yi, Jinhee 
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 introduce also two parametrizations hk,n and h'k,n of the thetafunction 4q . For q=e2piz , Im z > 0, define 4q : =fq,q=n =infinityinfinityqn2 =:q30,2z , where q3 is classical theta function. For any positive real numbers n and k, define hk,n=4ep n/k k1/44ep nk=q 30,n/k k1/4q30, nk and h'k,n=4 e2pn/k k1/44e2p nk =q30,1+2n/ kk1/4q 30,1+2nk . We show how they are connected with rk,n, r'k,n and RamanujanWeber class invariants and give some new thetafunction identities. In addition, we establish some formulas for hk,n and h'k,n by using those thetafunction identities and find some values of hk,n and h'k,n . Finally, we offer explicit formulas for 4enp and 4enp for any positive real numbers n. We give some examples. 
Issue Date:  2001 
Type:  Text 
Language:  English 
Description:  157 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 2001. 
URI:  http://hdl.handle.net/2142/86780 
Other Identifier(s):  (MiAaPQ)AAI3017261 
Date Available in IDEALS:  20150928 
Date Deposited:  2001 
This item appears in the following Collection(s)

Dissertations and Theses  Mathematics

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