Vacuum stability, string density of states and the Riemann zeta function

A Zero Density Result for the Riemann Zeta Function

N(σ, T ) ≤ 4.9(3T ) 8 3 (1−σ) log5−2σ(T ) + 51.5 log T, for σ ≥ 0.52 and T ≥ 2000. We discuss a generalization of the method used in these two results which yields an explicit bound of a similar shape while also improving the constants. Furthermore, we present the effect of these improvements on explicit estimates for the prime counting function ψ(x). This is joint work with Habiba Kadiri and N...

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...

Mollifying the Riemann Zeta-function

The Theory of the Riemann Zeta-function

Supercomputers and the Riemann Zeta Function

The Riemann Hypothesis, which specifies the location of zeros of the Riemann zeta function, and thus describes the behavior of primes, is one of the most famous unsolved problems in mathematics, and extensive efforts have been made over more than a century to check it numerically for large sets of cases. Recently a new algorithm, invented by the speaker and A. Scho . . nhage, has been implement...