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

References to SciGraph publications

  • 2012-04. Pseudodeformations in MATHEMATISCHE ZEITSCHRIFT
  • 2004-08. K(1)-local topological modular forms in INVENTIONES MATHEMATICAE
  • 1979-02. Eigenvalues of Hecke operators on SL(2, Z) in MATHEMATISCHE ANNALEN
  • 2009. The Arithmetic of Elliptic Curves in NONE
  • 1988. Arithmetic of p-adic Modular Forms in NONE
  • 1981-06. Congruences for eigenvalues of hecke operators on SL2 (Z) in MANUSCRIPTA MATHEMATICA
  • 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

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