Exploring theq-Riemann zeta function andq-Bernoulli polynomials

The Arakawa–kaneko Zeta Function and Poly-bernoulli Polynomials

The purpose of this paper is to introduce a generalization of the Arakawa–Kaneko zeta function and investigate their special values at negative integers. The special values are written as the sums of products of Bernoulli and poly-Bernoulli polynomials. We establish the basic properties for this zeta function and their special values.

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...

Lagrangians with Riemann Zeta Function

We consider construction of some Lagrangians which contain the Riemann zeta function. The starting point in their construction is p-adic string theory. These Lagrangians describe some nonlocal and nonpolynomial scalar field models, where nonlocality is controlled by the operator valued Riemann zeta function. The main motivation for this research is intention to find an effective Lagrangian for ...

Mollifying the Riemann Zeta-function

ON THE TWISTED q-ZETA FUNCTIONS AND q-BERNOULLI POLYNOMIALS

One purpose of this paper is to define the twisted q-Bernoulli numbers by using p-adic invariant integrals on Zp. Finally, we construct the twisted q-zeta function and q-L-series which interpolate the twisted q-Bernoulli numbers.