The minima of quadratic forms and the behavior of Epstein and Dedekind zeta functions

DOI10.1016/0022-314X(80)90062-1zbMath0432.10010MaRDI QIDQ1138571

Audrey A. Terras

Publication date: 1980

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

positivityEpstein zeta-functionDedekind zeta-functionpositive definite quadratic formALGOL procedurecomputation of incomplete gamma functionsincomplete gamma expansion

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Zeta functions and (L)-functions of number fields (11R42) Hurwitz and Lerch zeta functions (11M35) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

Related Items

The height of the Leech lattice, On the location of the zero-free half-plane of a random Epstein zeta function, On the universality of the Epstein zeta function, Saturating unitarity bounds at U-duality symmetric points, On the value distribution of the Epstein zeta function in the critical strip, Expected Riesz energy of some determinantal processes on flat tori, Non-vanishing of class group L-functions for number fields with a small regulator, Generation of off-critical zeros for hypercubic Epstein zeta functions, On the value distribution and moments of the Epstein zeta function to the right of the critical strip, Crystal Symmetry Viewed as Zeta Symmetry, Minima of Epstein's zeta function and heights of flat tori, On the minima and convexity of Epstein zeta function, On the zero-distribution of Epstein zeta-functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The principle of the theory of nonstandard functional equations for Dirichlet functions, consequences and applications of it
• Real zeroes of Epstein's zeta function for ternary positive definite quadratic forms
• The determination of incomplete gamma functions through analytic integration
• On automorphic forms for the general linear group
• Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen
• A simple proof of the functional equation of a certain L-function
• Artin-root numbers and normal integral bases for quaternion fields
• Hlawka's theorem in the geometry of numbers
• The analytic theory of algebraic numbers
• L-Functions of a Quadratic Form
• On the Group of Integral Automorphs of a Positive Definite Quadratic Form
• Bessel Series Expansions of the Epstein Zeta Function and the Functional Equation
• On Epstein's zeta function
• L-functions and character sums for quadratic forms (I)
• On the zeros of Epstein's zeta function