University of Illinois Urbana-Champaign

Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms

Bialek, Paul Richard

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https://hdl.handle.net/2142/22301

Description

Title
Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms
Author(s)
Bialek, Paul Richard
Issue Date
1995
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
  • "In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\sb4, E\sb4/E\sb6$ and other functions involving the Eisenstein series $E\sb4, E\sb6$ and $E\sbsp{2}{*}$. These formulas are stated, without proof, in a three-page manuscript published with his ""lost notebook."""
  • In the second part of this thesis, we prove five series identities of Ramanujan which arise from Eisenstein series. These identities are stated, without proof, in the unorganized portion of his second notebook.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/22301
Copyright and License Information
Copyright 1995 Bialek, Paul Richard

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