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arXiv · 1506.07416

Central limit theorem for Artin $L$-functions

Peter J. Cho·Henry H. Kim
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Abstract

We show that the sum of the traces of Frobenius elements of Artin $L$-functions in a family of $G$-fields satisfies the Gaussian distribution under certain counting conjectures. We prove the counting conjectures for $S_4$ and $S_5$-fields. We also show central limit theorem for modular form $L$-functions with the trivial central character with respect to congruence subgroups as the level goes to infinity.

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Peter J. Cho, Henry H. Kim. 2015-06-24. Central limit theorem for Artin $L$-functions. https://arxiv.org/abs/1506.07416

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