Related papers: Asymptotics for multilinear averages of multiplica…

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain…

We study the limiting behavior of multiple ergodic averages involving sequences of integers that satisfy some regularity conditions and have polynomial growth. We show that for "typical" choices of Hardy field functions $a(t)$ with…

A compilation of new results on the asymptotic behaviour of the Humbert functions $\Psi_1$ and $\Psi_2$, and also on the Appell function $F_2$, is presented. As a by-product, we confirm a conjectured limit which appeared recently in the…

We show that p-harmonic functions in the plane satisfy a nonlinear asymptotic mean value property for p>1. This extends previous results of Manfredi and Lindqvist for certain range of p's.

The Hardy operator has all the monomial functions as eigenvectors. We study bounded operators on L^2 that take monomial functions to multiples of other monomials, with a shifted exponent. We prove that they all leave the space of functions…

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…

In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

In this paper, we prove asymptotic expansions of generalized partial theta functions with a nonprincipal Dirichlet character and relate these expansions to certain $L$-series.

In this paper, we investigate the asymptotic properties of the generalised trigonometric integral $\operatorname{ti}(a, z, \alpha)$ and its associated modulus and phase functions for large complex values of $z$. We derive asymptotic…

This paper explores the asymptotic behaviour of the radii of convexity and uniform convexity for normalized Bessel functions with respect to large order. We provide detailed asymptotic expansions for these radii and establish recurrence…

Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic…

We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…

The refined asymptotic expansion of the confluent hypergeometric function $M(a,b,z)$ on the Stokes line $\arg\,z=\pi$ given in {\it Appl. Math. Sci.} {\bf 7} (2013) 6601--6609 is employed to derive the correct exponentially small…

Let v be a multiplicative arithmetic function with support of positive asymptotic density. We prove that for any not identically zero arithmetic function f such that \sum_{f(n) \neq 0} 1 / n < \infty, the support of the Dirichlet…

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…

In this note, we give a detailed proof of an asymptotic for averages of coefficients of a class of degree three $L$-functions which can be factorized as a product of a degree one and a degree two $L$-functions. We emphasize that we can…

We provide an asymptotic expansion for the mean-value of the logarithm of the middle prime factor of an integer, defined according to multiplicity or not, thus generalising a recent study of McNew, Pollack, and Singha Roy. This yields an…

Several uniform asymptotics expansions of the Weber parabolic cylinder functions are considered, one group in terms of elementary functions, another group in terms of Airy functions. Starting point for the discussion are asymptotic…