Skip to main content
SpringerLink
Log in

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

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chinta G., Diaconu A.: Determination of a GL3 cuspform by twists of central L-values. IMRN 2005, 2941–2967 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  2. Goldfeld D.: Analytic and arithmetic theory of Poincare series. Societe Mathematique de France, Asterisque 61, 95–107 (1979)

    MATH  MathSciNet  Google Scholar 

  3. Iwaniec H.: Topics in Classical Automorphic Forms, Graduate Studies in Mathematics 17. American Mathematical Society, Providence (1997)

    Google Scholar 

  4. Kowalski E., Michel P., VanderKam J.: Rankin–Selberg L-functions in the level aspect. Duke Math. J. 114(1), 123–191 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Luo W.: Special L-values of Rankin–Selberg convolutions. Math. Ann. 314(3), 591–600 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Luo W., Ramakrishnan D.: Determination of modular forms by twists of critical L-values. Invent. Math. 130(2), 371–398 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Merel, L.: Symboles de Manin et valeurs de fonctions L, Algebra, Arithmetic, and Geometry, In: Yuri, Z., Yuri, G. (eds.) Honor of Manin, Y. I., Progress in Mathematics, vol. 269, 270. Tschinkel (2009, in press)

  8. Oberhettinger F.: Tables of Mellin Transforms. Springer, New York (1974)

    MATH  Google Scholar 

  9. Piatetski-Shapiro, I.: Multiplicity one theorems, Automorphic Forms, Representations and L-Functions, In: Proceedings of the Symposium on Pure Mathematics, XXXIII, American Mathematical Society (1979)

  10. Titchmarsh, E.C.: The theory of the Riemann zeta-function, 2nd edn, Heath-Brown, D. R. (ed.) The Clarendon Press, Oxford University Press, New York, pp. x+412, ISBN: 0-19-853369-1 (1986)

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, 1, Homi Bhabha Road, Mumbai, 400005, India

    Satadal Ganguly & Jyoti Sengupta

  2. Department of Mathematics, Brown University, Providence, RI, 02912, USA

    Jeffrey Hoffstein

Authors
  1. Satadal Ganguly
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey Hoffstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jyoti Sengupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeffrey Hoffstein.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ganguly, S., Hoffstein, J. & Sengupta, J. Determining modular forms on \({SL_2(\mathbb{Z})}\) by central values of convolution L-functions. Math. Ann. 345, 843–857 (2009). https://doi.org/10.1007/s00208-009-0380-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00208-009-0380-2

Keywords

Search

Navigation