On signatures of elliptic curves and modular forms

In [ 4 ], the first and second authors studied the signatures of Dirichlet characters and elliptic curves. In this paper we improve their lower bound estimates in the case of elliptic curves. We also introduce and investigate integral and interval d -constant signatures for cusp forms, and prove low...

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Bibliographic Details
Published inThe Ramanujan journal Vol. 60; no. 2; pp. 505 - 516
Main Authors Dąbrowski, Andrzej, Pomykała, Jacek, Pujahari, Sudhir
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2023
Springer Nature B.V
Subjects
Combinatorics
Curves
Cusps
Dirichlet problem
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Lower bounds
Mathematics
Mathematics and Statistics
Number Theory
Signatures
11G05
Signature
11F30
Elliptic curve
Modular form
11G30
Dirichlet character
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ISSN1382-4090
1572-9303
DOI10.1007/s11139-022-00678-x

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Summary:In [ 4 ], the first and second authors studied the signatures of Dirichlet characters and elliptic curves. In this paper we improve their lower bound estimates in the case of elliptic curves. We also introduce and investigate integral and interval d -constant signatures for cusp forms, and prove lower bound results for the number of twisted cusp forms having positive or negative signatures.
Bibliography:ObjectType-Article-1
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ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-022-00678-x