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An additive problem in the Fourier coefficients of cusp forms

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Abstract.

 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.

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA (e-mail: gharcos@math.princeton.edu), , , , , , US

    Gergely Harcos

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  1. Gergely Harcos
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Received: 2 October 2001 / Revised version: 9 September 2002 / Published online: 28 March 2003

Mathematics Subject Classification (2000): Primary 11F30, 11F37; Secondary 11M41.

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Harcos, G. An additive problem in the Fourier coefficients of cusp forms. Math. Ann. 326, 347–365 (2003). https://doi.org/10.1007/s00208-003-0421-1

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  • DOI: https://doi.org/10.1007/s00208-003-0421-1

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