相关论文: Moments of restricted divisor functions
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
The moments of central values of families of L-functions have recently attracted much attention and, with the work of Keating and Snaith, there are now precise conjectures for their limiting values. We develop a simple method to establish…
In this paper we study counting functions representing the number of solutions of systems of linear inequalities which arise in the theory of Diophantine approximation. We develop a method that allows us to explain the random-like behavior…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
We demonstrate a simple analytic argument that may be used to bound the Levy concentration function of a sum of independent random variables. The main application is a version of a recent inequality due to Rudelson and Vershynin, and its…
In this article, we investigate high moments of zeta sums $\sum_{n\le x}n^{i t}$. We show unconditional lower bounds for them.
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…
We apply a classical mathematical problem, the moment problem, with its related mathematical achievements, to the study of the parton distribution function (PDF) in hadron physics, and propose a strategy to sieve the moments of the PDF by…
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
We obtain a good upper bound on the number of solutions of a diophantine equation arising from a strictly convex sequences of real numbers.
Without assuming the Northcott property we provide an upper bound on the number of "big solutions" of a special system of Diophantine inequalities over proper adelic curves. This system is interesting since it is a stronger version Roth's…
We prove a lower bound of the correct order of magnitude in the conductor aspect for small rational moments of Drichlet $L$-functions. Such bounds require new techniques, which is visible from the relationship to non-vanishing results for…
We discuss the problem of finding optimal exponents in Diophantine estimates involving one real number and, in some cases where such an exponent is known, present some properties of the corresponding extremal numbers.
We estimate the lattice sums arising in the context of the integer point counting in polyhedra.
Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured and…
The paper investigates solutions of the fractional hyperbolic diffusion equation in its most general form with two fractional derivatives of distinct orders. The solutions are given as spatial-temporal homogeneous and isotropic random…
Let $A\subset \N_{+}$ and by $P_{A}(n)$ denotes the number of partitions of an integer $n$ into parts from the set $A$. The aim of this paper is to prove several result concerning the existence of integer solutions of Diophantine equations…
We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the…
We characterize the existence of the Lebesgue integrable solutions of the truncated problem of moments in several variables on unbounded supports by the existence of some maximum entropy -- type representing densities and discuss a few…
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…