Congruences modulo prime powers of Hecke eigenvalues in level 1 View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Nadim Rustom

ABSTRACT

We continue the study of strong, weak, and dc-weak eigenforms introduced by Chen, Kiming, and Wiese. We completely determine all systems of Hecke eigenvalues of level 1 modulo 128, showing there are finitely many. This extends results of Hatada and can be considered as evidence for the more general conjecture formulated by the author together with Kiming and Wiese on finiteness of systems of Hecke eigenvalues modulo prime powers at any fixed level. We also discuss the finiteness of systems of Hecke eigenvalues of level 1 modulo 9, reducing the question to the finiteness of a single eigenvalue. Furthermore, we answer the question of comparing weak and dc-weak eigenforms and provide the first known examples of non-weak dc-weak eigenforms. More... »

PAGES

10

Journal

TITLE

Research in Number Theory

ISSUE

1

VOLUME

5

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40993-018-0147-5

DOI

http://dx.doi.org/10.1007/s40993-018-0147-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111058897


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