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

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Title: Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms
Author(s): Bialek, Paul Richard
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: 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.
Issue Date: 1995
Type: Text
Language: English
URI: http://hdl.handle.net/2142/22301
Rights Information: Copyright 1995 Bialek, Paul Richard
Date Available in IDEALS: 2011-05-07
Identifier in Online Catalog: AAI9522080
OCLC Identifier: (UMI)AAI9522080
 

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