On Cramér's theorem for general Euler products with functional equation

DOI10.1007/BF01459509zbMath0789.11054MaRDI QIDQ1318139

Serge Lang, Jay A. Jorgenson

Publication date: 12 April 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165139

zbMATH Keywords

Riemann surfacesfunctional equationasymptotic expansionRiemann zeta-functioneta-invariantrank one symmetric spacesEuler sumregularized productsfunctions of Selberg typeladder theoremMillson-Shintani zeta- functionSelberg zeta-functionsspectral theory of manifolds

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Zeta functions and (L)-functions of number fields (11R42) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Dirichlet series, exponential series and other series in one complex variable (30B50) Special classes of entire functions of one complex variable and growth estimates (30D15)

Related Items (14)

Zeta determinant for double sequences of spectral type ⋮ Heat-kernel expansion on noncompact domains and a generalized zeta-function regularization procedure ⋮ On theta type functions associated with the zeros of the Selberg zeta functions ⋮ Explicit formula for the hyperbolic scattering determinant ⋮ Convergence theorems for relative spectral functions on hyperbolic Riemann surfaces of finite volume ⋮ On Cartier-Voros type Selberg trace formula for congruence subgroups of \(\text{PSL} (2,\mathbb{R})\) ⋮ Extension of analytic number theory and the theory of regularized harmonic series from Dirichlet series to Bessel series ⋮ Guinand's theorem and functional equations for the Cramér functions ⋮ Elliptic factors of Selberg zeta functions ⋮ Elliptic factors of Selberg zeta functions ⋮ An explicit formula and its application to the Selberg trace formula ⋮ Universality of the Selberg zeta-function forthe modular group ⋮ Superzeta functions, regularized products, and the Selberg zeta function on hyperbolic manifolds with cusps ⋮ ON THE DISTRIBUTION OF ZEROS OF THE DERIVATIVE OF SELBERG’S ZETA FUNCTION ASSOCIATED TO FINITE VOLUME RIEMANN SURFACES

Cites Work

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