An analogue of Wilton's formula and values of Dedekind zeta functions

TL;DR

This paper extends Wilton's formula to Dedekind zeta functions, providing new expressions for their products and values at positive integers for various number fields, enhancing understanding of their properties.

Contribution

It introduces analogues of Wilton's formula for Dedekind zeta functions and derives new expressions for their values at positive integers across different number fields.

Findings

Derived formulas for Dedekind zeta function products

Expressed Dedekind zeta values at positive integers

Applicable to real and quadratic number fields

Abstract

J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We find analogous expressions for the product of two Dedekind zeta functions and then use these expressions to find some expressions for Dedekind zeta values attached to arbitrary real as well as quadratic number fields at any positive integer.