Related papers: A new approach to gaps between zeta zeros

In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.

In this article, with a new approach, which is not discussed in the literature yet, the limit of the Riemann zeta function or Euler-Riemann zeta function is approximately explored by applying Dirichlet's rearrangement theorem for absolutely…

In his groundbreaking work on pair correlation, Montgomery analyzed the distribution of the differences $\gamma'-\gamma$ between ordinates $\gamma$ of the nontrivial zeros of the Riemann zeta function, assuming the Riemann Hypothesis. In…

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…

We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the…

In this work, we present a non-linear difference equation for calculation of the zeros of the Riemann's zeta-function on the critical line. Our proposed non-linear map uses the Lambert W function and it can be easily implemented in a…

We refine a previous work of K. Matsumoto and H. Ishikawa, obtaining an asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial in the critical strip (1/4<$\sigma$<1/2), by obtaining an…

In this paper, first by employing inequalities derived from the Opial inequality due to David Boyd with best constant, we will establish new unconditional lower bounds for the gaps between the zeros of the Riemann zeta function. Second, on…

We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero…

Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem in 1973 concerning the pair correlation of zeros of the Riemann zeta-function and applied this to prove that at least $2/3$ of the zeros are simple. In this paper, we…

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of…

Let $\gamma$ denote imaginary parts of complex zeros of the Riemann zeta-function $\zeta(s)$. Certain sums over the $\gamma$'s are evaluated, by using the function $G(s) = \sum_{\gamma>0}\gamma^{-s}$ and other techniques. Some integrals…

By using the related results in the WZ theory, a new (as far as I know) formula for the values of Dirichlet beta function $\beta (s) = \sum\limits_{n = 1}^{+ \infty} {\frac{(-1)^{n - 1}}{(2n - 1)^s}} $ (where $Re(s) > 0$) at odd positive…

This is a reworked version of the paper. An idea that allows us to circumvent limitations of previous approaches is not to apply arithmetic-geometric mean inequality and the second moment asymptotics to the entire segment $[1/2-a/\log…

In this series we examine the calculation of the $2k$th moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper is concerned with the precise…

We obtain the product for the auxiliary function $\mathop{\mathcal R}(s)$ and study some related functions as its phase $\omega(t)$ at the critical line. The function $\omega(t)$ determines the zeros of $\zeta(s)$ on the critical line. We…

We investigate the distribution of large values of the Riemann zeta function $\zeta(s)$ in the strip $1/2<\re s<1$. For any fixed $\re s=\sigma\in(1/2,1)$, we obtain an improved distribution function of large values of $|\zeta(\sigma+\i…

We investigate explicit extreme values of the argument of the Riemann zeta-function in short intervals. As an application, we improve the result of Conrey and Turnage-Butterbaugh concerning $r$-gaps between zeros of the Riemann…

For most values of parameters $\lambda$ and $\alpha$, the zeros of the Lerch zeta-function $L(\lambda, \alpha, s)$ are distributed very chaotically. In this paper we consider the special case of equal parameters $L(\lambda, \lambda, s)$ and…

Assuming the Riemann hypothesis, we obtain upper and lower bounds for moments of the Riemann zeta-function averaged over the extreme values between its zeros on the critical line. Our bounds are very nearly the same order of magnitude. The…