Prime geodesics and averages of the Zagier L-series

2019/12/11 by Olga Balkanova, Balkanova, Olga, Dmitry Frolenkov +3
Mathematics · #11M41 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary 11M36 #Secondary 11F72

paper · pdf · doi:10.48550/arxiv.1912.05277

openalex publication_date 2019/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Zagier L-series encode data of real quadratic fields. We study the average size of these L-series, and prove asymptotic expansions and omega results for the expansion. We then show how the error term in the asymptotic expansion can be used to obtain error terms in the prime geodesic theorem.

Related

• Distribution of prime geodesic traces
• The Prime Geodesic Theorem and Bounds for Character Sums
• Consequences of the Gross/Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p
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• The Prime Geodesic Theorem for the Picard Orbifold