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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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