相关论文: On the Montgomery-Odlyzko method regarding gaps be…

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 2.7327 times the average spacing and infinitely often they differ by at most 0.5154 times the…

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…

In this paper, we introduce the resonance-correlation method to study small gaps between consecutive zeros of the Riemann zeta-function. Our method is based on a synthesis of Montgomery's pair correlation approach and the Montgomery-Odlyzko…

We show that the generalized Riemann hypothesis implies that there are infinitely many consecutive zeros of the Riemann zeta function whose spacing is 2.9125 times larger than the average spacing. This is deduced from the calculation of the…

Feng and Wu introduced a new general coefficient sequence into Montgomery and Odlyzko's method for exhibiting irregularity in the gaps between consecutive zeros of $\zeta(s)$ assuming the Riemann Hypothesis. They used a special case of…

In this paper, we will employ the Opial and Wirtinger type inequalities to derive some conditional and unconditional lower bounds for the gaps between the zeros of the Riemann zeta-function. First, we prove (unconditionally) that the…

Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.

We prove that there exist infinitely many consecutive zeros of the Riemann zeta-function on the critical line whose gaps are greater than $3.18$ times the average spacing. Using a modification of our method, we also show that there are even…

Combining the mollifiers, we exhibit other choices of coefficients that improve the results on large gaps between the zeros of the Riemann zeta-function. Precisely, assuming the Generalized Riemann Hypothesis (GRH), we show that there exist…

Assuming the Generalized Riemann Hypothesis(GRH), we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 3.072 times the average spacing.

Assuming the Riemann Hypothesis, we improve on previous results by proving there are infinitely many zeros of the Riemann zeta-function whose differences are smaller than 0.50412 times the average spacing. To obtain this result, we…

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…

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…

In 2016, the first-named author introduced a formulation of the Alternative Hypothesis that assumes that consecutive zeros of the Riemann zeta-function are spaced at multiples of half of the average spacing, but does not assume that the…

We settle a conjecture of Farmer and Ki in a stronger form. Roughly speaking we show that there is a positive proportion of small gaps between consecutive zeros of the zeta-function $\zeta(s)$ if and only if there is a positive proportion…

We use the asymptotic large sieve, developed by the authors, to prove that if the Generalized Riemann Hypothesis is true, then there exist many Dirichlet L-functions that have a pair of consecutive zeros closer together than 0.37 times…

Let $0<\gamma_1\leq \gamma_2 \leq \cdots $ denote the ordinates of nontrivial zeros of the Riemann zeta function with positive imaginary parts. For $c>0$ fixed (but possibly small), $T$ large, and $\gamma_n\leq T$, we call a gap…

In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function $\zeta(s)$ (and other L-functions) using Montgomery's pair correlation approach. We use semidefinite programming to improve upon numerous…

Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assuming RH, at least $67.9\%$ of the nontrivial zeros are simple.…

Odlyzko has computed a data set listing more than $10^9$ successive Riemann zeros, starting at a zero number beyond $10^{23}$. The data set relates to random matrix theory since, according to the Montgomery-Odlyzko law, the statistical…