We study Ruelle’s type zeta and L-functions for a torsion free abelian group Γ of rank ν ≥ 2 defined via an Euler product. It is shown that the imaginary axis is a natural boundary of this zeta function when ν = 2, 4 and 8, and in particular, such a zeta function has no determinant expression. Thus, conversely, expressions like Euler’s product for the determinant of the Laplacians of the torus ...

1 1 Preliminaries 1 1.1 Function fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The zeta function . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Primes and Divisors . . . . . . . . . . . . . . . . . . . . 2 1.2.2 The Picard Group . . . . . . . . . . . . . . . . . . . . . . 5 1.2.3 Riemann-Roch . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Notation . . . . ...

The zeta potential of early hydration products of cement was found to be a key factor for superplasticizer adsorption. A highly positive zeta potential results in a strong superplasticizer adsorption whereas a negative zeta potential does not allow adsorption. Synthetic ettringite precipitated from solution shows a highly positive zeta potential, hence it adsorbs great amounts of negatively cha...

This paper investigates a new family of special functions referred to as hypergeometric zeta functions. Derived from the integral representation of the classical Riemann zeta function, hypergeometric zeta functions exhibit many properties analogous to their classical counterpart, including the intimate connection to Bernoulli numbers. These new properties are treated in detail and are used to d...

This paper investigates a generalization the classical Hurwitz zeta function. It is shown that many of the properties exhibited by this special function extends to class of functions called hypergeometric Hurwitz zeta functions, including their analytic continuation to the complex plane and a pre-functional equation satisfied by them. As an application, a formula for moments of hypergeometric H...

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some q-series identity for proving the zeta function has an Euler product and then, describe the location of zeros. We study further multi-variable and multi-parameter versions of the multiple finite Riemann zeta functions and their infinite cou...

Globin gene switching is a well-described model of eucaryotic developmental control. In the case of the human alpha-globin gene cluster, migration of erythropoietic activity from the embryonic yolk sac to the fetal liver is parallaled by the zeta-globin gene silencing and enhanced expression of the alpha-globin genes. To map critical cis determinants of this switch, the human zeta-globin gene, ...

The zeta-dimension of a set A of positive integers is Dimζ(A) = inf{s | ζA(s) < ∞}, where ζA(s) = ∑ n∈A n. Zeta-dimension serves as a fractal dimension on Z that extends naturally and usefully to discrete lattices such as Z, where d is a positive integer. This paper reviews the origins of zeta-dimension (which date to the eighteenth and nineteenth centuries) and develops its basic theory, with ...

Influence of aqueous phase properties and process parameters on kaolinite particle zeta potential was quantified by electrophoresis experiments. The results indicated that pH strongly altered the zeta potential of kaolinite and it decreases at the beginning and then increases in the range of pH = 2–13. The activity of different cations changes the zeta potential and has the following tendency o...