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arXiv · 2309.04186

The Prime Geodesic Theorem in Arithmetic Progressions

Dimitrios Chatzakos·Gergely Harcos·Ikuya Kaneko
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Abstract

We address the prime geodesic theorem in arithmetic progressions, and resolve conjectures of Golovchanski\u{\i}-Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced residue classes of a given modulus.

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Dimitrios Chatzakos, Gergely Harcos, Ikuya Kaneko. 2023-09-08. The Prime Geodesic Theorem in Arithmetic Progressions. https://doi.org/10.1093/imrn%2Frnae198

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