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The Prime Geodesic Theorem in Arithmetic Progressions
Published 8 Sep 2023 in math.NT | (2309.04186v1)
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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