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


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.


Modular Form Cusp Form Dirichlet Series Trace Formula Automorphic Form 
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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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