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1 results

  • The orthogonality of Hecke eigenvalues

  • Henryk Iwaniec, Xiaoqing Li
  • Journal:
    Compositio Mathematica / Volume 143 / Issue 3 / May 2007
    Published online by Cambridge University Press:
    04 December 2007, pp. 541-565
    Print publication:
    May 2007
    • Article
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  • 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.