Distribution of prime numbers and the discrete spectrum of the Laplace operator

DOI10.1070/IM8999zbMath1453.58008OpenAlexW3018756797MaRDI QIDQ5135767

D. A. Popov

Publication date: 23 November 2020

Published in: Izvestiya: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/im8999

zbMATH Keywords

modular groupprime numbersChebyshev psi-functionspectrum of the Laplace operator

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Cites Work

• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• Relationship between the discrete and resonance spectrum for the Laplace operator on a noncompact hyperbolic Riemann surface
• SELBERG'S TRACE FORMULA FOR THE HECKE OPERATOR GENERATED BY AN INVOLUTION, AND THE EIGENVALUES OF THE LAPLACE-BELTRAMI OPERATOR ON THE FUNDAMENTAL DOMAIN OF THE MODULAR GROUP $ PSL(2,\mathbf{Z})$
• SPECTRAL THEORY OF AUTOMORPHIC FUNCTIONS, THE SELBERG ZETA-FUNCTION, AND SOME PROBLEMS OF ANALYTIC NUMBER THEORY AND MATHEMATICAL PHYSICS
• The prime geodesic theorem
• The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function
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