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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 Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:We introduce also two parametrizations hk,n and h'k,n of the theta-function 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=4e-p n/k k1/44e-p nk=q 30,-n/k k1/4q30, -nk and h'k,n=4 -e-2pn/k k1/44-e-2p nk =q30,1+2-n/ kk1/4q 30,1+2-nk . We show how they are connected with rk,n, r'k,n and Ramanujan-Weber class invariants and give some new theta-function identities. In addition, we establish some formulas for hk,n and h'k,n by using those theta-function identities and find some values of hk,n and h'k,n . Finally, we offer explicit formulas for 4-e-np and 4e-np 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 Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/86780
Other Identifier(s):(MiAaPQ)AAI3017261
Date Available in IDEALS:2015-09-28
Date Deposited:2001


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