Apéry-like numbers and families of newforms with complex multiplication View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

Alexis Gomez, Dermot McCarthy, Dylan Young

ABSTRACT

Using Hecke characters, we construct two infinite families of newforms with complex multiplication, one by Q(-3) and the other by Q(-2). The values of the p-th Fourier coefficients of all the forms in each family can be described by a single formula, which we provide explicitly. This allows us to establish a formula relating the p-th Fourier coefficients of forms of different weights, within each family. We then prove congruence relations between the p-th Fourier coefficients of these newforms at all odd weights and values coming from two of Zagier’s sporadic Apéry-like sequences. More... »

PAGES

5

References to SciGraph publications

  • 1985-04. On the Picard-Fuchs equation and the formal brauer group of certain ellipticK3-surfaces in MATHEMATISCHE ANNALEN
  • 2016-12. Divisibility properties of sporadic Apéry-like numbers in RESEARCH IN NUMBER THEORY
  • 2012-12. Sporadic sequences, modular forms and new series for 1/π in THE RAMANUJAN JOURNAL
  • 2002-10. On Dwork's accessory parameter problem in MATHEMATISCHE ZEITSCHRIFT
  • 2001. Gaussian Hypergeometric Series and Combinatorial Congruences in SYMBOLIC COMPUTATION, NUMBER THEORY, SPECIAL FUNCTIONS, PHYSICS AND COMBINATORICS
  • 1977. Galois representations attached to eigenforms with nebentypus in MODULAR FUNCTIONS OF ONE VARIABLE V
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40993-018-0145-7

    DOI

    http://dx.doi.org/10.1007/s40993-018-0145-7

    DIMENSIONS

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