In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

Recently, Storm [10] defined the Ihara-Selberg zeta function of a hypergraph, and gave two determinant expressions of it by the Perron-Frobenius operator of a digraph and a deformation of the usual Laplacian of a graph. We present a new determinant expression for the Ihara-Selberg zeta function of a hypergraph, and give a linear algebraic proof of Storm’s Theorem. Furthermore, we generalize the...

We further recall that under Selberg orthonormality conjecture, has unique factorization into primitive functions, the only primitive function with a pole at s = 1 is the Riemann zeta function ζ(s), and Fθ(s) is a primitive function if θ ∈R and if F ∈ are primitive and entire (see [4, Section 4]). We say a primitive function F ∈ is normal if θF = 0. Assuming Selberg orthonormality conjecture, w...

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Basic structure on symmetric spaces and Eisenstein series . . . . . . . . . . . . . . . . . 7 2. Harmonic analysis on groups and the Selberg trace formula . . . . . . . . . . . . . . . 11 3. Multiplicities of discrete series . . . . . . . . . . . . . . . . ...

Abstract We formulate a generalization of Riesz-type criteria in the setting L -functions belonging to Selberg class. obtain criterion which is sufficient for grand Riemann hypothesis (GRH) satisfying axioms class without imposing Ramanujan on their coefficients. also construct subclass and prove necessary GRH this subclass. Identities Ramanujan–Hardy–Littlewood type are established setting, sp...

In this paper, we will give a certain formula for the Riemann zeta function that expresses the Riemann zeta function by an infinte series consisting of KBessel functions. Such an infinite series expression can be regarded as an analogue of the Chowla-Selberg formula. Roughly speaking, the Chowla-Selberg formula is the formula that expresses the Epstein zeta-function by an infinite series consis...