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arXiv · 2011.07504

Probability density functions attached to random Euler products for automorphic $L$-functions

Masahiro Mine
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Abstract

In this paper, we study the value-distributions of $L$-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic $L$-functions with probabilistic models called the random Euler products. First, we prove the existence of probability density functions attached to the random Euler products. Then various mean values of automorphic $L$-functions are expressed as integrals involving the density functions. Moreover, we estimate the discrepancies between the distributions of values of automorphic $L$-functions and those of the random Euler products.

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Masahiro Mine. 2020-11-15. Probability density functions attached to random Euler products for automorphic $L$-functions. https://doi.org/10.1093/qmath/haab035

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