A Kronecker limit formula for indefinite zeta functions

Zeta Determinant for Double Sequences of Spectral Type and a Generalization of the Kronecker First Limit Formula

The Kronecker first limit formula in the number field K is an expression of the value of the constant term in the Laurent expansion at s = 1 of the partial Dedekind zeta function ζA(s), associated to an ideal class A of K (see Section 4.1 for details), and has deep applications in number theory. When K is the rational number field or an imaginary quadratic field such formulas are classical and ...

A Kronecker Limit Formula for Totally Real Fields and Arithmetic Applications

We establish a Kronecker limit formula for the zeta function ζF (s,A) of a wide ideal class A of a totally real number field F of degree n. This formula relates the constant term in the Laurent expansion of ζF (s,A) at s = 1 to a toric integral of a SLn(Z)-invariant function logG(Z) along a Heegner cycle in the symmetric space of GLn(R). We give several applications of this formula to algebraic...

Convolution Dirichlet Series and a Kronecker Limit Formula for Second-order Eisenstein Series

In this article we derive analytic and Fourier aspects of a Kronecker limit formula for second-order Eisenstein series. Let Γ be any Fuchsian group of the first kind which acts on the hyperbolic upper half-space H such that the quotient Γ\H has finite volume yet is non-compact. Associated to each cusp of Γ\H, there is a classically studied first-order non-holomorphic Eisenstein series E(s, z) w...

Indefinite Summation and the Kronecker Delta

Indefinite summation, together with a generalized version of the Kronecker delta, provide a calculus for reasoning about various polynomial functions that arise in combinatorics, such as the Tutte, chromatic, flow, and reliability polynomials. In this paper we develop the algebraic properties of the indefinite summation operator and the generalized Kronecker delta from an axiomatic viewpoint. O...

Nonholomorphic Eisenstein series, the Kronecker limit formula, and the hyperbolic Laplacian