Mathematische Annalen

, Volume 326, Issue 2, pp 347–365

An additive problem in the Fourier coefficients of cusp forms

  • Gergely Harcos

DOI: 10.1007/s00208-003-0421-1

Cite this article as:
Harcos, G. Math. Ann. (2003) 326: 347. doi:10.1007/s00208-003-0421-1


 We establish an estimate on sums of shifted products of Fourier coefficients coming from holomorphic or Maass cusp forms of arbitrary level and nebentypus. These sums are analogous to the binary additive divisor sum which has been studied extensively. As an application we derive, extending work of Duke, Friedlander and Iwaniec, a subconvex estimate on the critical line for L-functions associated to character twists of these cusp forms.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Gergely Harcos
    • 1
  1. 1.Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA (e-mail:

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