A complete Riemann zeta distribution and the Riemann hypothesis

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 ...

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...

Riemann Zeta Moments

The behavior of the Riemann zeta function () on the critical line Re() = 12 has been studied intensively for nearly 150 years. We start with a well-known

A Riemann zeta stochastic process

and thus be represented (for σ > 1 ) as a product of terms of the form exp(a(eibt − 1)), each of which is the characteristic function of a Poisson random variable with intensity a and values in the lattice kb, k = 0, 1, 2, . . . . Cf. Gnedenko and Kolmogorov [6, p. 75]. Faced with a family of “zeta distributions” indexed by parameter σ > 1 , one is led to ask for joint distributions, i.e., for ...