A note on prime zeta function and Riemann zeta function. Corrigendum

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...

Prime Number Theory and the Riemann Zeta-Function

Riemann ’ s zeta function and the prime number theorem

16 Riemann’s zeta function and the prime number theorem We now divert our attention from algebraic number theory to talk about zeta functions and L-functions. As we shall see, every global field has a zeta function that is intimately related to the distribution of its primes. We begin with the zeta function of the rational field Q, which we will use to prove the prime number theorem. We will ne...

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...

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 ...