On a two-variable zeta function for number fields.

DOI10.5802/aif.1939zbMath1106.11036arXivmath/0104176OpenAlexW1625870364MaRDI QIDQ1864241

Eric M. Rains, Jeffrey C. Lagarias

Publication date: 17 March 2003

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0104176

zbMATH Keywords

functional equationinfinitely divisible distributionszeta functionsArakelov divisors

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Entire functions of several complex variables (32A15)

Related Items (10)

Functional equations for regularized zeta-functions and diffusion processes ⋮ On the Epstein zeta function and the zeros of a class of Dirichlet series ⋮ Gluing of graphs and their Jacobians ⋮ On infinitely divisible distributions related to the Riemann hypothesis ⋮ Certain extensions of results of Siegel, Wilton and Hardy ⋮ On the irreducibility of the two variable zeta-function for curves over finite fields. ⋮ Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions ⋮ A modified Riemann zeta distribution in the critical strip ⋮ A Note on Jacobians, Tutte Polynomials, and Two-Variable Zeta Functions of Graphs ⋮ A complete Riemann zeta distribution and the Riemann hypothesis

Cites Work

• Über Betragsmittelwerte und die Fourier-Koeffizienten der ganzen automorphen Formen
• The Fourier coefficients of automorphic forms on horocyclic groups. II
• On the distribution of zeros of linear combinations of Euler products
• Über automorphe Orthogonalfunktionen und die Konstruktion der automorphen Formen von positiver reeller Dimension
• On the expansion of the partition functions in a series
• Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions
• Magnitude of the Fourier coefficients of automorphic forms of negative dimension
• Turan Inequalities and Zeros of Dirichlet Series Associated with Certain Cusp Forms
• Effectivity of Arakelov divisors and the theta divisor of a number field
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