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Mathematische Annalen

, Volume 345, Issue 4, pp 843–857 | Cite as

Determining modular forms on \({SL_2(\mathbb{Z})}\) by central values of convolution L-functions

  • Satadal Ganguly
  • Jeffrey Hoffstein
  • Jyoti Sengupta
Article

Abstract

We show that a cuspidal normalized Hecke eigenform g of level one and even weight is uniquely determined by the central values of the family of Rankin– Selberg L-functions \({L(s, f\otimes g)}\) , where f runs over the Hecke basis of the space of cusp forms of level one and weight k with k varying over an infinite set of even integers.

Keywords

Modular Form Cusp Form Dirichlet Series Trace Formula Automorphic Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Satadal Ganguly
    • 1
  • Jeffrey Hoffstein
    • 2
  • Jyoti Sengupta
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchMumbaiIndia
  2. 2.Department of MathematicsBrown UniversityProvidenceUSA

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