A spectral interpretation of the zeros of the constant term of certain Eisenstein series

DOI10.1515/CRELLE.2008.049zbMath1230.11109arXivmath/0703340MaRDI QIDQ3524822

Werner Müller

Publication date: 15 September 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703340

zbMATH Keywords

spectral interpretationconstant term of non-normalized Eisenstein serieseigenvalues of self-adjoint operator

Mathematics Subject Classification ID

Zeta functions and (L)-functions of number fields (11R42) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (2)

Spectral zeta functions of graphs and the Riemann zeta function in the critical strip ⋮ Upper bound for the number of zeros of a meromorphic function outside a vertical line and applications

Cites Work

• On a result of G. Pólya concerning the Riemann \(\xi\)-function
• The Riemann hypothesis for certain integrals of Eisenstein series
• A complete determination of the complex quadratic fields of class-number one
• Generators and relations for certain special linear groups
• Zeros of the constant term in the Chowla–Selberg formula
• The Determinant of the Eisenstein Matrix and Hilbert Class Fields

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