Square integrals of the logarithmic derivatives of Selberg’s zeta functions in the critical strip

DOI10.1142/S1793042123500379WikidataQ114071736 ScholiaQ114071736MaRDI QIDQ5881022

Yasufumi Hashimoto

Publication date: 9 March 2023

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.07816

zbMATH Keywords

Selberg zeta functioncritical stripsquare integral

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Cites Work

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• Distribution of eigenvalues for the modular group
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• ON ANALOGUES OF THE ARTIN FACTORIZATION FORMULAS IN THE SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS CONNECTED WITH INDUCED REPRESENTATIONS OF FUCHSIAN GROUPS
• Prime geodesic theorem.
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• Correlations of multiplicities in length spectra for congruence subgroups
• The prime geodesic theorem
• THE MEAN SQUARE OF THE LOGARITHMIC DERIVATIVE OF THE SELBERG ZETA FUNCTION FOR COCOMPACT DISCRETE SUBGROUPS
• Sums of Kloosterman sums in the prime geodesic theorem
• A mean value theorem for closed geodesics on congruence surfaces
• Class numbers of indefinite binary quadratic forms
• The correlation between multiplicities of closed geodesics on the modular surface
• Selberg's zeta function for the modular group in the critical strip

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