Prime geodesic theorem for the Picard manifold

被引：5

作者：

Balkanova, Olga ^{[1
]}

Frolenkov, Dmitry ^{[2
]}

机构：

[1] Chalmers Univ Technol, Dept Math Sci, Chalmers Tvargata 3, S-41296 Gothenburg, Sweden

[2] Russian Acad Sci, Steklov Math Inst, 8 Gubkina St, Moscow 119991, Russia

来源：

ADVANCES IN MATHEMATICS | 2020年 / 375卷

关键词：

Spectral exponential sum; Prime geodesic theorem; Picard manifold; FORMULA; SUBCONVEXITY;

D O I：

10.1016/j.aim.2020.107377

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma = PSL(2,Z vertical bar i vertical bar) be the Picard group and H-3 be the three-dimensional hyperbolic space. We study the Prime Geodesic Theorem for the quotient Gamma\H-3, called the Picard manifold, obtaining an error term of size O(X3/2+theta/2+epsilon), where theta denotes a subconvexity exponent for quadratic Dirichlet L-functions defined over Gaussian integers. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：42

共 50 条

[11] ON THE ERROR TERM IN THE PRIME GEODESIC THEOREM
Avdispahic, Muharem
Gusic, Dzenan
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (02) : 367 - 372
[12] The prime geodesic theorem in square mean
Balog, Antal
Biro, Andras
Harcos, Gergely
Maga, Peter
JOURNAL OF NUMBER THEORY, 2019, 198 : 239 - 249
[13] The Prime Geodesic Theorem in Arithmetic Progressions
Chatzakos, Dimitrios
Harcos, Gergely
Kaneko, Ikuya
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2024, 2024 (20) : 13180 - 13190
[14] Prime geodesic theorem for the modular surface
Avdispahic, Muharem
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2020, 49 (02): : 505 - 509
[15] AN EXISTENCE THEOREM OF A CLOSED GEODESIC ON A MANIFOLD WITH BOUNDARY
SCOLOZZI, D
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1985, 4A (03): : 451 - 457
[16] Gallagherian Prime Geodesic Theorem in Higher Dimensions
Muharem Avdispahić
Zenan Šabanac
Bulletin of the Malaysian Mathematical Sciences Society, 2020, 43 : 3019 - 3026
[17] On the prime geodesic theorem for SL4
Gušić D.
International Journal of Circuits, Systems and Signal Processing, 2020, 14 : 42 - 48
[18] Prime geodesic theorem for arithmetic compact surfaces
Koyama, SY
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 1998, 1998 (08) : 383 - 388
[19] On Koyama's refinement of the prime geodesic theorem
Avdispahic, Muharem
PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 2018, 94 (03) : 21 - 24
[20] A prime geodesic theorem for SL4
Deitmar, Anton
Pavey, Mark
ANNALS OF GLOBAL ANALYSIS AND GEOMETRY, 2008, 33 (02) : 161 - 205

← 1 2 3 4 5 →