On the Occurrence of Hecke Eigenvalues and a Lacunarity Question of Serre

Nahid Walji

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arXiv · 1411.2058

On the Occurrence of Hecke Eigenvalues and a Lacunarity Question of Serre

Nahid Walji

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Abstract

Let πbe a unitary cuspidal automorphic representation for GL(n) over a number field. We establish upper bounds on the number of Hecke eigenvalues of πequal to a fixed complex number. For GL(2), we also determine upper bounds on the number of Hecke eigenvalues with absolute value equal to a fixed number γ; in the case γ=0, this answers a question of Serre. These bounds are then improved upon by restricting to non-dihedral representations. Finally, we obtain analogous bounds for a family of cuspidal automorphic representations for GL(3).

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Nahid Walji. 2014-11-07. On the Occurrence of Hecke Eigenvalues and a Lacunarity Question of Serre. https://arxiv.org/abs/1411.2058

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