The Prime Geodesic Theorem in Arithmetic Progressions-Reference-Cited by-同舟云学术

The Prime Geodesic Theorem in Arithmetic Progressions

Published:2024-09-12 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Chatzakos Dimitrios¹,Harcos Gergely²,Kaneko Ikuya³

Affiliation:

1. Department of Mathematics , School of Natural Sciences, University of Patras, Panepistimioupoli Patron 265 04, Patras, Greece

2. Alfréd Rényi Institute of Mathematics , POB 127, Budapest H-1364, Hungary

3. The Division of Physics , Mathematics and Astronomy, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA

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.

Funder

ELKE of the University of Patras

Rényi Intézet Lendület Automorphic Research Group

National Research, Development and Innovation Office

Publisher

Oxford University Press (OUP)

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnae198/59100676/rnae198.pdf

Reference43 articles.

1. Prime geodesic theorem in the 3-dimensional hyperbolic space;Balkanova;Trans. Amer. Math. Soc.,2019

2. Sums of Kloosterman sums in the prime geodesic theorem;Balkanova;Q. J. Math.,2019

3. Prime geodesic theorem for the Picard manifold;Balkanova;Adv. Math.,2020

4. Prime geodesics and averages of the Zagier $L$-series;Balkanova;Math. Proc. Camb. Philos. Soc.,2022

5. “The prime geodesic theorem in square mean;Balog;J. Number Theory,2019