On zeros of characteristic p zeta function

On The Riemann Hypothesis For The Characteristic p Zeta Function

Simple Zeros of the Riemann Zeta-function

Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.

On the Multiplicity of Zeros of the Zeta-function

A b s t r a c t. Several results are obtained concerning multiplicities of zeros of the Riemann zeta-function ζ(s). They include upper bounds for multiplicities, showing that zeros with large multiplicities have to lie to the left of the line σ = 1. A zero-density counting function involving multiplicities is also discussed. AMS Subject Classification (1991): 11M06

On the distribution of zeros of the Hurwitz zeta-function

Assuming the Riemann hypothesis, we prove asymptotics for the sum of values of the Hurwitz zeta-function ζ(s, α) taken at the nontrivial zeros of the Riemann zeta-function ζ(s) = ζ(s, 1) when the parameter α either tends to 1/2 and 1, respectively, or is fixed; the case α = 1/2 is of special interest since ζ(s, 1/2) = (2s − 1)ζ(s). If α is fixed, we improve an older result of Fujii. Besides, we...

Zeros of the Riemann Zeta-Function on the Critical Line

It was shown by Selberg [3] that the Riemann Zeta-function has at least cT log T zeros on the critical line up to height T, for some positive absolute constant c. Indeed Selberg’s method counts only zeros of odd order, and counts each such zero once only, regardless of its multiplicity. With this in mind we shall write γ̂i for the distinct ordinates of zeros of ζ(s) on the critical line of odd m...