Articles publiés
Distribution of prime geodesic traces
Antonius Deitmar1
1Mathematisches Institut, auf der Morgenstelle 10, 72076 Tübingen, Germany
Confluentes Mathematici, Tome 18 (2026), pp. 25-30

This note complements a recent paper of Chatzakos, Harcos and Kaneko [3]. We use a Dirichlet style Prime Geodesic Theorem to improve on the error term estimate in loc. cit. at the cost of lowering the resolution. The proof relies on the Selberg trace formula.

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DOI : 10.5802/cml.103
Classification : 11F72, 11M36
Keywords: prime geodesic theorem, Selberg trace formula, Selberg zeta function

Antonius Deitmar  1

1 Mathematisches Institut, auf der Morgenstelle 10, 72076 Tübingen, Germany
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Antonius Deitmar. Distribution of prime geodesic traces. Confluentes Mathematici, Tome 18 (2026), pp. 25-30. doi: 10.5802/cml.103
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[1] Muharem Avdispahić A prime geodesic theorem of Gallagher type for Riemann surfaces, Anal. Math., Volume 46 (2020) no. 1, pp. 25-38 | DOI | Zbl | MR

[2] William Casselman Quadratic forms over finite fields, 2011 (https://www.math.ubc.ca/~cass/siegel/FiniteFields.pdf)

[3] Dimitrios Chatzakos; Gergely Harcos; Ikuya Kaneko The prime geodesic theorem in arithmetic progressions, Int. Math. Res. Not., Volume 2024 (2024) no. 20, pp. 13180-13190 | DOI | Zbl | MR

[4] William Fulton; Joe Harris Representation theory: a first course, Graduate Texts in Mathematics: Readings in Mathematics, 129, Springer, 1991, xvi+551 pages | DOI | MR | Zbl

[5] Dennis A. Hejhal The Selberg trace formula for ${\mathrm{PSL}}\,(2,{\mathbb{R}})$. Vol. 2, Lecture Notes in Mathematics, 1001, Springer, 1983, viii+806 pages | DOI | Zbl | MR

[6] Wenzhi Luo; Zeév Rudnick; Peter C. Sarnak On Selberg’s eigenvalue conjecture, Geom. Funct. Anal., Volume 5 (1995) no. 2, pp. 387-401 | DOI | Zbl | MR

[7] Kannan Soundararajan; Matthew P. Young The prime geodesic theorem, J. Reine Angew. Math., Volume 676 (2013), pp. 105-120 | DOI | MR | Zbl

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