University of Illinois Urbana-Champaign

The Construction and Applications of Modular Equations

Yi, Jinhee

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/86780

Description

Title
The Construction and Applications of Modular Equations
Author(s)
Yi, Jinhee
Issue Date
2001
Doctoral Committee Chair(s)
Berndt, Bruce C.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
Graduation Semester
2001
Type of Resource
text
Permalink
http://hdl.handle.net/2142/86780

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics