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Algorithms for Computing Congruences Between Modular Forms

Title: Algorithms for Computing Congruences Between Modular Forms.
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Name(s): Heaton, Randy, author
Agashe, Amod, professor co-directing dissertation
Van Hoeij, Mark, professor co-directing dissertation
Capstick, Simon, university representative
Aldrovandi, Ettore, committee member
Department of Mathematics, degree granting department
Florida State University, degree granting institution
Type of Resource: text
Genre: Text
Issuance: monographic
Date Issued: 2012
Publisher: Florida State University
Florida State University
Place of Publication: Tallahassee, Florida
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: Let $N$ be a positive integer. We first discuss a method for computing intersection numbers between subspaces of $S_{2}(Gamma_{0}(N),C)$. Then we present a new method for computing a basis of q-expansions for $S_{2}(Gamma_{0}(N),Q)$, describe an algorithm for saturating such a basis in $S_{2}(Gamma_{0}(N),Z)$, and show how these results have applications to computing congruence primes and studying cancellations in the conjectural Birch and Swinnerton-Dyer formula.
Identifier: FSU_migr_etd-4904 (IID)
Submitted Note: A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Degree Awarded: Summer Semester, 2012.
Date of Defense: June 28, 2012.
Keywords: Elliptic Curves, Modular Forms, Number Theory
Bibliography Note: Includes bibliographical references.
Advisory Committee: Amod Agashe, Professor Co-Directing Dissertation; Mark van Hoeij, Professor Co-Directing Dissertation; Simon Capstick, University Representative; Ettore Aldrovandi, Committee Member.
Subject(s): Mathematics
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_migr_etd-4904
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Host Institution: FSU

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Heaton, R. (2012). Algorithms for Computing Congruences Between Modular Forms. Retrieved from http://purl.flvc.org/fsu/fd/FSU_migr_etd-4904