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The Prime Geodesic Theorem in Arithmetic Progressions
Dimitrios Chatzakos, Gergely Harcos, Ikuya Kaneko
Source abstract
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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