Abstract. In this short paper we present a simple method for deriving a remarkable functional identity for Riemann’s Zeta Function. The connections between some functional equations obtained implicitly by Leonhard Euler in his work ”Remarques sur un beau rapport entre les series des puissances tant directes que reciproques (E 352)” in Memoires de l’Academie des Sciences de Berlin 17, (1768) per...

We derive an expression for the value ζQ(3) of the spectral zeta function ζQ(s) studied in [10, 11] for the non-commutative harmonic oscillator defined in [17] using a Gaussian hypergeometric function. In this study, two sequences of rational numbers, denoted J̃2(n) and J̃3(n), which can be regarded as analogues of the Apéry numbers, naturally arise and play a key role in obtaining the expression...

In this note, we apply the group-theoretic method to study Artin’s conjecture, and introduce the notations of nearly nilpotent groups and nearly supersolvable groups to answer of a question of Arthur and Clozel. As an application, we show that Artin’s conjecture is valid for all nearly supersolvable Galois extensions of number fields as well as all solvable Frobenius extensions.

The aim of this paper is to define an n− 1-cocycle σ on GLn(Q) with values in a certain space D of distributions on Af \ {0}. Here Af denotes the ring of finite adèles of Q, and the distributions take values in the Laurent series C((z1, . . . , zn)). This cocycle can be used to evaluate special values of Artin L-functions on number fields at negative integers. The construction generalizes that ...

Abstract. In this paper we shall develop a theory of (extended) double shuffle relations of Euler sums which generalizes that of multiple zeta values (see Ihara, Kaneko and Zagier, Derivation and double shuffle relations for multiple zeta values. Compos. Math. 142 (2)(2006), 307–338). After setting up the general framework we provide some numerical evidence for our two main conjectures. At the ...

To an arbitrary intersection of exceptional varieties of an embedded resolution we associate a nite number of congruences between naturally occurring multiplicities. This theory generalizes previous results concerning just one exceptional variety. Moreover we describe precise equalities which imply the congruences and we give some applications on the poles of Igusa's local zeta function.

For a large smooth particle with charges at the surface, the electrophoretic mobility is proportional to the zeta potential, which is related to the charge density by the Gouy-Chapman theory of the diffuse double layer. This classical model adequately describes the dependence of the electrophoretic mobility of phospholipid vesicles on charge density and salt concentration, but it is not applica...

We provide a number of results that can be used to derive approximations for the Euler product representation of the zeta function of an arbitrary algebraic function field. Three such approximations are given here. Our results have two main applications. They lead to a computationally suitable algorithm for computing the class number of an arbitrary function field. The ideas underlying the clas...

biopolymers are environmental friendly sources as renewable and sustainable substituents for petroleum-based polymers. application of these polymers is common in variety of industries including papermaking. herbalexudate gums have been used in papermaking industry for decades, especially paper recycling. in this study, gum polysaccharide exudates from baridje plant  (ferula gummosa) extracted a...

This is the first report implementing combined density gradient centrifugation/Zeta (DGC/Zeta) sperm selection procedure for a couple with eleven previous intra cytoplasmic sperm injection/ in vitro fertilization (ICSI/IVF) failure cycles. Semen analysis was carried out according to World Health Organization criteria. Protamine deficiency, DNA fragmentation and morphology were assessed by chrom...