The sign changes of Fourier coefficients of Eisenstein series

Title:
The sign changes of Fourier coefficients of Eisenstein series
Authors:
Linowitz, Benjamin; Thompson, Lola
Abstract:
In this paper we prove a number of theorems that determine the extent to which the signs of the Hecke eigenvalues of an Eisenstein newform determine the newform. We address this problem broadly and provide theorems of both individual and statistical nature. Many of these results are Eisenstein series analogs of well-known theorems for cusp forms. For instance, we determine how often the pth Fourier coefficients of an Eisenstein newform begin with a fixed sequence of signs Formula Not Shown . Moreover, we prove the following variant of the strong multiplicity-one theorem: an Eisenstein newform is uniquely determined by the signs of its Hecke eigenvalues with respect to any set of primes with density greater than Formula Not Shown .
Citation:
Linowitz, Benjamin, and Lola Thompson. 2015. "The sign changes of Fourier coefficients of Eisenstein series." The Ramanujan Journal 37(2): 223-241.
Publisher:
Springer Verlag
DATE ISSUED:
2015-06
Department:
Mathematics
Type:
Article
PUBLISHED VERSION:
10.1007/s11139-013-9552-5
Additional Links:
http://link.springer.com/10.1007/s11139-013-9552-5
PERMANENT LINK:
http://hdl.handle.net/11282/614614

Full metadata record

DC FieldValue Language
dc.contributor.authorLinowitz, Benjaminen
dc.contributor.authorThompson, Lolaen
dc.date.accessioned2016-06-24T16:03:27Z-
dc.date.available2016-06-24T16:03:27Z-
dc.date.issued2015-06-
dc.identifier.citationLinowitz, Benjamin, and Lola Thompson. 2015. "The sign changes of Fourier coefficients of Eisenstein series." The Ramanujan Journal 37(2): 223-241.en
dc.identifier.issn1382-4090-
dc.identifier.urihttp://hdl.handle.net/11282/614614-
dc.description.abstractIn this paper we prove a number of theorems that determine the extent to which the signs of the Hecke eigenvalues of an Eisenstein newform determine the newform. We address this problem broadly and provide theorems of both individual and statistical nature. Many of these results are Eisenstein series analogs of well-known theorems for cusp forms. For instance, we determine how often the pth Fourier coefficients of an Eisenstein newform begin with a fixed sequence of signs Formula Not Shown . Moreover, we prove the following variant of the strong multiplicity-one theorem: an Eisenstein newform is uniquely determined by the signs of its Hecke eigenvalues with respect to any set of primes with density greater than Formula Not Shown .en
dc.language.isoen_USen
dc.publisherSpringer Verlagen
dc.identifier.doi10.1007/s11139-013-9552-5-
dc.relation.urlhttp://link.springer.com/10.1007/s11139-013-9552-5en
dc.subject.departmentMathematicsen_US
dc.titleThe sign changes of Fourier coefficients of Eisenstein seriesen_US
dc.typeArticleen
dc.identifier.journalThe Ramanujan Journalen
dc.subject.keywordEigenformsen_US
dc.subject.keywordFourier coefficientsen_US
dc.subject.keywordSign changesen_US
dc.identifier.volume37en_US
dc.identifier.issue2en_US
dc.identifier.startpage233en_US
dc.rightsArchived with thanks to The Ramanujan Journalen
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