An additive problem in the Fourier coefficients of cusp forms

Harcos, Gergely (2003) An additive problem in the Fourier coefficients of cusp forms. Mathematische Annalen, 326 (2). pp. 347-365. ISSN 0025-5831 (print), 1432-1807 (online)

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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 analoaous 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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