The orthogonality of Hecke eigenvalues

Henryk Iwaniec, Xiaoqing Li

Type: Article

Publication Date: 2007-05-01

Citations: 22

DOI: https://doi.org/10.1112/s0010437x07002679

Abstract

In this paper, we study the orthogonalities of Hecke eigenvalues of holomorphic cusp forms. An asymptotic large sieve with an unusually large main term for cusp forms is obtained. A family of special vectors formed by products of Kloosterman sums and Bessel functions is constructed for which the main term is exceptionally large. This surprising phenomenon reveals an interesting fact: that Fourier coefficients of cusp forms favor the direction of products of Kloosterman sums and Bessel functions of compatible type.

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