An extension ofq-zeta function

An extension of q-zeta function

We will define the extension of q-Hurwitz zeta function due to Kim and Rim (2000) and study its properties. Finally, we lead to a useful new integral representation for the q-zeta function. 1. Introduction. Let 0 < q < 1 and for any positive integer k, define its q-analogue [k] q = (1 − q k)/(1 − q). Let C be the field of complex numbers. The q-zeta function due

An Extension of the Thermodynamic Formalism Approach to Selberg's Zeta Function for General Modular Groups

The Segre Zeta Function of an Ideal

We define a power series associated with a homogeneous ideal in a polynomial ring, encoding information on the Segre classes defined by extensions of the ideal in projective spaces of arbitrarily high dimension. We prove that this power series is rational, with poles corresponding to generators of the ideal, and with numerator of bounded degree and with nonnegative coefficients. We also prove t...

The Probabilistic Zeta Function

This paper is a summary of results on the PG(s) function, which is the reciprocal of the probabilistic zeta function for finite groups. This function gives the probability that s randomly chosen elements generate a group G, and information about the structure of the group G is embedded in it.

q-Riemann zeta function

We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)= ∑∞ n=1(qn(s−1)/[n]s), 0< q < 1, s ∈ C. In this paper, we give q-Bernoulli numbers which can be viewed as interpolation of the above q-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some...