Prime geodesic theorem for the modular group
Yasufumi Hashimoto
TL;DR
This paper improves the error term exponent in the prime geodesic theorem for the modular group from 25/36 to 9/13, advancing the understanding of prime geodesics in hyperbolic geometry.
Contribution
It refines the error term exponent in the prime geodesic theorem for the modular group, building on prior methods by Soundararajan and Young.
Findings
Error term exponent improved to 9/13
Enhanced understanding of prime geodesics
Advancement over previous exponent 25/36
Abstract
Soundararajan and Young (2013) proposed a new approach to improve the error term of the prime geodesic theorem for the modular group and actually obtained the exponent 25/36 of the error term. In the present paper, we sharpen it to 9/13.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Analytic Number Theory Research