The holomorphic flow of the Riemann zeta function

Corrigendum to "The holomorphic flow of the Riemann zeta function"

Theorem 4.5 of [2], describing the topological type of the zeros of the flow ṡ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gökcek for pointing out the error to us. In some circumstances the types will never be the same. Indeed, it appears to be unlikely that a fixed formal relationship will exist bet...

The holomorphic flow of the Riemann zeta function

The flow of the Riemann zeta function, ṡ = ζ(s), is considered, and phase portraits are presented. Attention is given to the characterization of the flow lines in the neighborhood of the first 500 zeros on the critical line. All of these zeros are foci. The majority are sources, but in a small proportion of exceptional cases the zero is a sink. To produce these portraits, the zeta function was ...

Mollifying the Riemann Zeta-function

The Theory of the Riemann 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...