Rankin–Cohen brackets and Serre derivatives as Poincaré series View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-12

AUTHORS

Brandon Williams

ABSTRACT

We give expressions for the Serre derivatives of Eisenstein and Poincaré series as well as their Rankin–Cohen brackets with arbitrary modular forms in terms of the Poincaré averaging construction, and derive several identities for the Ramanujan tau function as applications.

PAGES

37

References to SciGraph publications

  • 2018-12. Poincaré square series for the Weil representation in THE RAMANUJAN JOURNAL
  • 2008. Elliptic Modular Forms and Their Applications in THE 1-2-3 OF MODULAR FORMS
  • 1994-02. Modular forms and differential operators in PROCEEDINGS - MATHEMATICAL SCIENCES
  • 1991-05. Cusp forms and special values of certain Dirichlet series in MATHEMATISCHE ZEITSCHRIFT
  • 2015-04. The adjoint of some linear maps constructed with the Rankin–Cohen brackets in THE RAMANUJAN JOURNAL
  • 1977. Modular forms whose fourier coefficients involve zeta-functions of quadratic fields in MODULAR FUNCTIONS OF ONE VARIABLE VI
  • Journal

    TITLE

    Research in Number Theory

    ISSUE

    4

    VOLUME

    4

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s40993-018-0130-1

    DOI

    http://dx.doi.org/10.1007/s40993-018-0130-1

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1106706112


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