A UNIFIED METHOD FOR EVALUATING RIEMANN ZETA FUNCTIONS, DIRICHLET SERIES, ASSOCIATED CLAUSEN FUNCTIONS, OTHER ALLIED SERIES, AND NEW CLASSES OF INFINITE SERIES

Multiple Dirichlet Series and Moments of Zeta and L–functions

This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments o...

A Numerical Integration Method by Using Generalized Series of Functions

The Riemann Zeta and Allied Functions

Relative order and type of entire functions represented by Banach valued Dirichlet series in two variables

In this paper, we introduce the idea of relative order and type of entire functions represented by Banach valued Dirichlet series of two complex variables to generalize some earlier results. Proving some preliminary theorems on the relative order, we obtain sum and product theorems and we show that the relative order of an entire function represented by Dirichlet series is the same as that of i...

Igusa zeta functions and motivic generating series

Proefschrift ingediend tot het behalen van de graad van Doctor in de Wetenschappen december 2004 ii Introduction Let f be a polynomial in Z[x], x = (x 1 ,. .. , x m), defining a hypersurface X 0 in A m Z. Igusa's Monodromy Conjecture predicts an intriguing relationship between the arithmetic properties of f , and the topology of the (not necessarily reduced) complex hypersurface X 0 = X 0 × Spe...