Riemann hypothesis and Zeta-Function

On The Riemann Hypothesis For The Characteristic p Zeta Function

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...

Other Representations of the Riemann Zeta Function and an Additional Reformulation of the Riemann Hypothesis

New expansions for some functions related to the Zeta function in terms of the Pochhammer's polynomials are given (coe cients bk, dk, d̂k and ˆ̂ dk). In some formal limit our expansion bk obtained via the alternating series gives the regularized expansion of Maslanka for the Zeta function. The real and the imaginary part of the function on the critical line is obtained with a good accuracy up to ...

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