Related papers: Small gaps and small spacings between zeta zeros

Study of the level curves the real part of $\eta(s)=0$ and imaginary part of $\eta(s)=0$, for $\eta(s)=\pi^{-s/2}\Gamma(s/2)\zeta^\prime(s)$ gives a new classification of the zeros of $\zeta(s)$ and of $\zeta^\prime(s)$. Numerical evidence…

Given an infinite subset $\mathcal A \subseteq\mathbb N$, let $A$ denote its smallest $N$ elements. There is a rich and growing literature on the question of whether for typical $\alpha\in[0,1]$, the pair correlations of the set $\alpha A…

Radiation symmetry is briefly reviewed, along with its historical, experimental, computational, and theoretical relevance. A sketch of the proof of a theorem for radiation zeros is used to highlight the connection between gauge-boson…

Let Q be a nondegenerate quadratic form, and L is a nonzero linear form of dimension d>3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x),L(x)):x\in Z^d} is dense in R^2 provided that Q and L satisfy some…

A Master equation has been previously obtained which allows the analytic integration of a fairly large family of functions provided that they possess simple properties. Here, the properties of this Master equation are explored, by extending…

The loss of criticality in the form of weak first-order transitions or the end of the conformal window in gauge theories can be described as the merging of two fixed points that move to complex values of the couplings. When the complex…

The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann zeta function which are sufficiently strong to break the density hypothesis in a nontrivial part of the critical strip. Apart from…

We present exact kinematic consistency relations for cosmological structures that do not vanish at equal times and can thus be measured in surveys. These rely on cross-correlations between the density and velocity, or momentum, fields.…

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

An equivalence is proven between the Riemann Hypothesis and the speed of convergence to 1/zeta(2) of the probability that two independent random variables following the same geometric distribution are coprime integers, when the parameter of…

We explore different variants of the random phase approximation (RPA) to the correlation energy derived from closed-shell ring-diagram approximations to coupled cluster doubles theory. We implement these variants in range-separated…

The symmetries of the $t=1$ and $t=0$ pair-fields are different. The consequences for rotational spectra are discussed. For $t=1$, the concept of spontaneous breaking and subsequent restoration of the isospin symmetry turns out to be…

We seek to understand how the technical definition of Lehmer pair can be related to more analytic properties of the Riemann zeta function, particularly the location of the zeros of $\zeta^\prime(s)$. Because we are interested in the…

It is pointed out that there are now known four very close pairs of QSOs with separations < 5 arcsec and very different redshifts. Several estimates of the probability that they are accidental configurations range between 10^{-7} and 3.5 x…

Assuming the Riemann hypothesis and Montgomery's Pair Correlation Conjecture, we investigate the distribution of the sequences $(\log|\zeta(\rho+z)|)$ and $(\arg\zeta(\rho+z)).$ Here $\rho=\frac12+i\gamma$ runs over the nontrivial zeros of…

In this work, we investigate the experimental correlation between the pairing gap values and two important observables in the study of nuclear structure (two neutron separation energies and thermal-neutron capture cross-sections). To this…

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

This paper shows that one needs to be careful when making statements on potential links between correlation and coskewness. Specifically, we first show that, on the one hand, it is possible to observe any possible values of coskewness among…

Using equations, governing np pairing correlations in S=1, T=0 pairing channel (PRC 63 (2001) 021304(R)), it is shown that at low densities equations for the energy gap in the spectrum of quasiparticles and chemical potentials of protons…

In this paper, we present results on the uniqueness of the real zeros of the Hurwitz zeta function in given intervals. The uniqueness in question, if the zeros exist, has already been proved for the intervals $(0,1)$ and $(-N, -N+1)$ for $N…