The first eigenvalue problem and tensor products of zeta functions

DOI10.3792/PJAA.80.35zbMath1065.11035OpenAlexW2092809250MaRDI QIDQ1764320

Shin-ya Koyama

Publication date: 24 February 2005

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

Full work available at URL: https://projecteuclid.org/euclid.pja/1116442239

zbMATH Keywords

Selberg conjecturesymmetric power \(L\)-functiontensor product of zeta-functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (2)

Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic 3-manifolds ⋮ The prime geodesic theorem for \(\mathrm{PSL}2(\mathbb{Z}[i)\) and spectral exponential sums]

Cites Work

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• The arithmetic and geometry of some hyperbolic three manifolds
• Derivatives of multiple sine functions
• La conjecture de Weil. I
• Functorial products for \(\text{GL}_2\times \text{GL}_3\) and the symmetric cube for \(\text{GL}_2\).
• On Selberg's eigenvalue conjecture
• On the Holomorphy of Certain Dirichlet Series
• Multiple sine functions
• Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂
• Multiple zeta functions: the double sine function and the signed double Poisson summation formula
• Problems in the theory of automorphic forms to Salomon Bochner in gratitude

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