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arXiv · 1901.03824

On Kuznetsov-Bykovskii's formula of counting prime geodesics

Giacomo Cherubini·Han Wu·Gergely Zábrádi
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Abstract

We generalize a formula on the counting of prime geodesics, due to Kuznetsov-Bykovskii, used in the work of Soundararajan-Young on the prime geodesic theorem. The method works over any number field and for any congruence subgroup. We give explicit computation in the cases of principal and Hecke subgroups.

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Giacomo Cherubini, Han Wu, Gergely Zábrádi. 2019-01-12. On Kuznetsov-Bykovskii's formula of counting prime geodesics. https://doi.org/10.1007/s00209-021-02808-5

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