相关论文: An exponentially averaged Vasyunin formula
V. I. Vasyunin has introduced special sequences of step functions related to the strong Nyman-Beurling criterion that converge pointwise to 1 in $[1,\infty)$. We show here that the first and simplest such sequence considered by Vasyunin…
The decreasing enumeration of the points of a Poisson random measure whose mean measure has finite survival function on the positive half-axis can be represented as a non-increasing function of the jump times of a standard Poisson process.…
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis. These sums contain the M\"obius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably…
A new proof of the Weyl limit point-limit circle criterion is obtained, with systematic emphasis on Sobolev-space methods.
We show that the Eynard-Orantin topological recursion, in conjunction with simple auxiliary equations, can be used to calculate all correlation functions of supereigenvalue models.
We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the M\"obius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the M\"obius function.…
We conjecture the connection between $su$ and $so$ members of universal, in Vogel's sense, multiplets. The key element is the notion of the {\it vertical componentwise sum} $\oplus_v$ of Young diagrams. Representations in the decomposition…
Recently we proved (EPRSY, ERSTVY, ESY4, ESYY, EYY, EYY2, EYYrigi) that the eigenvalue correlation functions of a general class of random matrices converge, weakly with respect to the energy, to the corresponding ones of Gaussian matrices.…
We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…
Reciprocity in dyadic interactions is common and a topic of interest across disciplines. In some cases, reciprocity may be expected to be more or less prevalent among certain kinds of dyads. In response to interest among researchers in…
We study sets of recurrence, in both measurable and topological settings, for actions of $(\mathbb{N},\times)$ and $(\mathbb{Q}^{>0},\times)$. In particular, we show that autocorrelation sequences of positive functions arising from…
The main aim of the paper is to present a general version of the Fourier Tauberian theorem for monotone functions. This result, together with Berezin's inequality, allows us to obtain a refined version the Li-Yau estimate for the counting…
We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
We prove a combinatorial formula for the alternating descent polynomials of type A and B. Combining with Josuat-Verg\`es' combinatorial interpretation for Hoffman's derivative polynomials for tangent and secant functions, we obtain a…
The $\mathrm{U}(1)$ Chern-Simons theory can be extended to a topological $\mathrm{U}(1)^n$ theory by taking a combination of Chern-Simons and BF actions, the mixing being achieved with the help of a collection of integer coupling constants.…
In this article we show that the use of Deligne-Beilinson cohomology in the context of the $U(1)$ BF theory on a closed 3-manifold $M$ yields a discrete $\Z_N$ BF theory whose partition function is an abelian TV invariant of $M$. By…
This paper presents a family of rapidly convergent summation formulas for various finite sums of analytic functions. These summation formulas are obtained by applying a series acceleration transformation involving Stirling numbers of the…
Let $\bX=\{X_n\}_{n\geq 1}$ and $\bY=\{Y_n\}_{n\geq 1}$ be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums $$ \psi_n(\bX,\bY)=\sum_{i=1}^nX_iY_i/V_n,\quad…
We give a new heuristic for all of the main terms in the quotient of products of L-functions averaged over a family. These conjectures generalize the recent conjectures for mean values of L-functions. Comparison is made to the analogous…