On zeta functions associated with quadratic forms of variable coefficients

Zeta Functions for Equivalence Classes of Binary Quadratic Forms

They are sums of zeta functions for prehomogeneous vector spaces and generalizations of Epstein zeta functions. For the rational numbers and imaginary quadratic fields one can define these functions also for SL(2, ^-equivalence, which for convenience we call 1equivalence. The second function arises in the calculation of the Selberg trace formula for integral operators on L(PSL(2, (!?)\H) where ...

About the Cover: Zeta-functions Associated with Quadratic Forms in Adolf Hurwitz’s Estate

The first published proof of key analytic properties of zeta-functions associated with quadratic forms is due to Paul Epstein [2] in 1903 (submitted January 1902). The corresponding name “Epstein zeta-functions” was introduced by Edward Charles Titchmarsh in his article [15] from 1934; soon after, this terminology became common through influential articles of Max Deuring and Carl Ludwig Siegel....

On Zeta Functions of Orthogonal Groups of Single-class Positive Definite Quadratic Forms

Representations of Hecke–Shimura rings of integral single-class positive definite quadratic forms on relevant spaces of harmonic forms are considered, and the problem of simultaneous diagonalization of the corresponding Hecke operators is investigated. Explicit relations are deduced between zeta functions of the single-class quadratic forms in two and four variables corresponding to the harmoni...

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Quadratic Functions, Optimization, and Quadratic Forms