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arXiv · 1805.04330

The equidistribution of L-functions of twists by Witt vector Dirichlet characters over function fields

Will Sawin
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Abstract

Katz showed that the L-functions of all Dirichlet characters of F_q(t), with conductor a fixed power of a degree one prime, are equidistributed in the limit as q goes to infinity. We generalize this statement to the L-functions of twists of an arbitrary Galois representation by Dirichlet characters, including independence of the L-functions of twists of different representations by the same Dirichlet character. A similar generalization, without the independence statement, for characters with squarefree conductor, was proven by Hall, Keating, and Roditty-Gershon.

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Will Sawin. 2018-05-11. The equidistribution of L-functions of twists by Witt vector Dirichlet characters over function fields. https://arxiv.org/abs/1805.04330

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