Zeros, eigenvalues and arithmetic

DOI10.3792/pjaa.60.22zbMath0554.10015OpenAlexW2056977308MaRDI QIDQ759788

Akio Fujii

Publication date: 1984

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.60.22

zbMATH Keywords

exponential sumseigenvaluesasymptotic behaviourhyperbolic Laplacianentire functionsspecial valueszeta-functions

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

On Cartier-Voros type Selberg trace formula for congruence subgroups of \(\text{PSL} (2,\mathbb{R})\) ⋮ Spectral exponential sums on hyperbolic surfaces ⋮ An additive problem of prime numbers. III ⋮ Zeta zeros, Hurwitz zeta functions and L(1,\(\chi\) ) ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums] ⋮ Eigenvalues of the Laplace-Beltrami operator and the von-Mangoldt function

Cites Work

• Remainder term in the Weyl-Selberg asymptotic formula
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Formules de Poisson avec reste
• 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})$
• A Summation Formula in the Theory of Prime Numbers
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
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