Euler products of Selberg zeta functions in the critical strip

DOI10.1007/s11139-022-00550-yOpenAlexW2892837632MaRDI QIDQ2675252

Shin-ya Koyama, Ikuya Kaneko

Publication date: 21 September 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.10140

zbMATH Keywords

Euler productsSelberg eigenvalue conjectureprime geodesic theoremSelberg zeta functionsgeneralised Riemann hypothesisdeep Riemann hypothesis

Mathematics Subject Classification ID

Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Related Items (4)

Spectral exponential sums on hyperbolic surfaces ⋮ The second moment for counting prime geodesics ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums] ⋮ Chebyshev's bias against splitting and principal primes in global fields

Cites Work

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• Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II
• Arithmetic expressions of Selberg's zeta functions for congruence subgroups
• Highly composite numbers. Annotated by Jean-Louis Nicolas and Guy Robin
• Arithmetic forms of Selberg zeta functions with applications to prime geodesic theorem
• On Selberg's eigenvalue conjecture
• Quantum ergodicity of eigenfunctions on \(\text{PSL}_ 2(\mathbb{Z}) \backslash H^ 2\)
• Density theorems and the mean value of arithmetical functions in short intervals
• The Euler product for the Riemann zeta-function in the critical strip
• ON ANALOGUES OF THE ARTIN FACTORIZATION FORMULAS IN THE SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS CONNECTED WITH INDUCED REPRESENTATIONS OF FUCHSIAN GROUPS
• Prime geodesic theorem.
• Partial Euler Products on the Critical Line
• The prime geodesic theorem
• Class numbers of indefinite binary quadratic forms

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