Eisenstein Series, Analogues of the Rogers -Ramanujan Functions, and Partition Identities
Hahn, Heekyoung
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https://hdl.handle.net/2142/86836
Description
Title
Eisenstein Series, Analogues of the Rogers -Ramanujan Functions, and Partition Identities
Author(s)
Hahn, Heekyoung
Issue Date
2004
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
Chapter 4 is devoted to finding new partition identities inspired by the work of O. Kolberg and S. Ramanujan. We use functions studied by N. J. Fine and R. J. Evans to construct analogues of modular equations, and then derive new identities satisfied by n=0infinity p(ln + k) qn, where p(n) is the ordinary partition function, l is an odd prime, and 0 ≤ k ≤ (l - 1).
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