The Prime Geodesic Theorem in Arithmetic Progressions

Chatzakos, Dimitrios and Harcos, Gergely and Kaneko, Ikuya (2024) The Prime Geodesic Theorem in Arithmetic Progressions. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024 (20). pp. 13180-13190. ISSN 1073-7928

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Abstract

We address the prime geodesic theorem in arithmetic progressions and resolve conjectures of Golovchanskiĭ–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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