Related papers: Unnormalized differences between zeros of L-functi…

We numerically study the statistical properties of differences of zeros of Riemann zeta function and L-functions predicted by the theory of the e\~ne product. In particular, this provides a simple algorithm that computes any non-real…

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…

We investigate the distribution of the zeros of partial sums of the Riemann zeta-function, sum_{n\leq X}n^{-s}, estimating the number of zeros up to height T, the number of zeros to the right of a given vertical line, and other aspects of…

Assuming the Riemann hypothesis, we show that a certain vertical distribution of the nontrivial zeros of the Riemann zeta-function is equivalent to the generalized Riemann hypothesis for Dirichlet $L$-functions. Furthermore, under both the…

We establish an unconditional asymptotic formula describing the horizontal distribution of the zeros of the derivative of the Riemann zeta-function. For $\Re(s)=\sigma$ satisfying $(\log T)^{-1/3+\epsilon} \leq (2\sigma-1) \leq (\log \log…

This paper studies the local spacings of deformations of the Riemann zeta function under certain averaging and differencing operations. For real h it considers A_h(s)= 1/2(xi(s+h)+ xi(s-h)) and B_h(s)=1/(2i)(xi(s+h)-xi(s-h)), where xi(s) is…

We continue our investigation of the distribution of the fractional parts of $a \gamma$, where $a$ is a fixed non-zero real number and $\gamma$ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We…

We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma'$, at large. We show, that independently of the location of the zeros, their differences have similar statistical properties. The distributions of…

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.5155 times the average spacing and infinitely often they differ by at least 2.69 times the average…

We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma^{'}$, at large distances. We show, that independently of the height, a subset of finite number of successive zeros knows the locations of lower level…

In the paper, we introduce $q$-deformations of the Riemann zeta function, extend them to the whole complex plane, and establish certain estimates of the number of roots. The construction is based on the recent difference generalization of…

Numerical investigations around a transformation of Landau's formula suggest certain statistical regularities in the distribution of zeros of the Riemann zeta function.

Fujii investigated the uniform distribution of various sequences associated with the non-trivial zeros of the Riemann zeta function by evaluating certain exponential sums over these zeros. In this paper, we present analogous results for a…

We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma^{'}$, at large. We show, that independently of the location of the zeros, i.e., even for zeros as high as $10^{23}$, their differences have similar…

We investigate the distribution of the fractional parts of ag, where a is a fixed non-zero real number and g runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. The revision includes several minor…

We introduce a new method to detect the zeros of the Riemann zeta function which is sensitive to the vertical distribution of the zeros. This allows us to prove there are few `half-isolated' zeros. By combining this with classical methods,…

Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…

We investigate the horizontal distribution of zeros of the derivative of the Riemann zeta function and compare this to the radial distribution of zeros of the derivative of the characteristic polynomial of a random unitary matrix. Both…

We improve the estimation of the distribution of the nontrivial zeros of Riemann zeta function $\zeta(\sigma+it)$ for sufficiently large $t$, which is based on an exact calculation of some special logarithmic integrals of nonvanishing…

It has been conjectured that the statistical properties of zeros of the Riemann zeta function near $z = 1/2 + \ui E$ tend, as $E \to \infty$, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite…