Persistent Link:
http://hdl.handle.net/10150/228631
Title:
A Classification of all Hecke Eigenform Product Identities
Author:
Johnson, Matthew Leander
Issue Date:
2012
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this dissertation, we give a complete classification and list all identities of the form h = fg, where f , g and h are Hecke eigenforms of any weight with respect to Γ₁(N). This result extends the work of Ghate [Gha02] who considered this question for eigenforms with respect to Γ₁(N), with N square-free and f and g of weight 3 or greater. We remove all restrictions on the level N and the weights of f and g. For N = 1 there are only 16 eigenform identities, which are classically known. We first give a new proof of the level N = 1 case. We then give a proof which classifies all such eigenform identities for all levels N > 1. The identities fall into two categories. There are two infinite families of identities, given in Table 7.2. There are 209 other identities, listed (up to conjugacy) in Table 7.1. Thus any eigenform identity h = f g with respect to Γ₁(N) is either conjugate to an identity in Table 7.1 or takes the form of an identity described in Table 7.2.
Type:
text; Electronic Dissertation
Keywords:
Modular Forms; Number Theory; Products; Mathematics; Eigenforms; Hecke
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Joshi, Kirti

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA Classification of all Hecke Eigenform Product Identitiesen_US
dc.creatorJohnson, Matthew Leanderen_US
dc.contributor.authorJohnson, Matthew Leanderen_US
dc.date.issued2012-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this dissertation, we give a complete classification and list all identities of the form h = fg, where f , g and h are Hecke eigenforms of any weight with respect to Γ₁(N). This result extends the work of Ghate [Gha02] who considered this question for eigenforms with respect to Γ₁(N), with N square-free and f and g of weight 3 or greater. We remove all restrictions on the level N and the weights of f and g. For N = 1 there are only 16 eigenform identities, which are classically known. We first give a new proof of the level N = 1 case. We then give a proof which classifies all such eigenform identities for all levels N > 1. The identities fall into two categories. There are two infinite families of identities, given in Table 7.2. There are 209 other identities, listed (up to conjugacy) in Table 7.1. Thus any eigenform identity h = f g with respect to Γ₁(N) is either conjugate to an identity in Table 7.1 or takes the form of an identity described in Table 7.2.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectModular Formsen_US
dc.subjectNumber Theoryen_US
dc.subjectProductsen_US
dc.subjectMathematicsen_US
dc.subjectEigenformsen_US
dc.subjectHeckeen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorJoshi, Kirtien_US
dc.contributor.committeememberJoshi, Kirtien_US
dc.contributor.committeememberCais, Brydenen_US
dc.contributor.committeememberLux, Klausen_US
dc.contributor.committeememberThakur, Dineshen_US
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