Universality of $L$-Functions over function fields

Abstract

We prove that the Dirichlet $L$-functions associated with Dirichlet characters in ${\mathbb{F}}_q[x]$ are universal. That is, given a modulus of high enough degree, $L$-functions with characters to this modulus can be found that approximate any given nonvanishing analytic function arbitrarily closely.

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References in corpus (1)

• Truncated Product Representations for $L$-Functions in the Hyperelliptic Ensemble