Related papers: Asymptotics of eigenvalue sums when some turning p…

Since the $\mathrm{Fibonacci}$ sequence has good properties, it's important in theory and applications, such as in combinatorics, cryptography, and so on. In this paper, for the generalized Fibonacci sequence…

A spectral problem is considered in a thin $3D$ graph-like junction that consists of three thin curvilinear cylinders that are joined through a domain (node) of the diameter $\mathcal{O}(\varepsilon),$ where $\varepsilon$ is a small…

Explicit representations of the eigenvalues of the peridynamic operator have been recently derived in [5]. These representations are given in terms of generalized hypergeometric functions. Asymptotic analysis of the hypergeometric functions…

We consider the fractional Laplacian on a domain and investigate the asymptotic behavior of its eigenvalues. Extending methods from semi-classical analysis we are able to prove a two-term formula for the sum of eigenvalues with the leading…

This work gives a general approach to the determination of the asymptotic behavior of the sums of functions of primes based on the distribution of primes. It refines the estimate of the remainder term of the asymptotic expansion of the sums…

Let $F(x)= \sum_{\nu\in\NN^d} F_\nu x^\nu$ be a multivariate power series with complex coefficients that converges in a neighborhood of the origin. Assume $F=G/H$ for some functions $G$ and $H$ holomorphic in a neighborhood of the origin.…

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…

In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…

The purpose of this paper is to obtain asymptotics of shifted sums of Hecke eigenvalue squares on average. We show that for $X^{\frac{2}{3}+\epsilon} < H <X^{1-\epsilon},$ there are constants $B_{h}$ such that $$ \sum_{X\leq n \leq 2X}…

We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…

We study local asymptotic properties of likelihood ratios of certain Heston models. We distinguish three cases: subcritical, critical and supercritical models. For the drift parameters, local asymptotic normality is proved in the…

A theorem about asymptotic estimation of multiple integral of a special type is proved for the case when the integrand peaks at the integration domain bound, but not at a point of extremum. Using this theorem the asymptotic expansion of the…

We combine the ideas of a Harish-Chandra--Howe local character expansion, which can be centred at an arbitrary semisimple element, and a Kim--Murnaghan asymptotic expansion, which so far has been considered only around the identity. We show…

Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving accuracy, and providing deeper insight into the underlying…

We establish asymptotic formulas for sums of reciprocals of primes in arithmetic progressions, generalizing recent results on multiple Mertens evaluations by Tenenbaum, Qi, and Hu. Specifically, for any fixed constant $K>0$, we derive…

We study asymptotic behavior of the bottom point of the spectrum of convolution type operators in environments with locally periodic microstructure. We show that its limit is described by an additive eigenvalue problem for Hamilton-Jacobi…

In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found…

In this paper we analyze the asymptotic behavior of several fractional eigenvalue problems by means of Gamma-convergence methods. This method allows us to treat different eigenvalue problems under a unified framework. We are able to recover…

The differential-equation eigenvalue problem associated with a recently-introduced Hamiltonian, whose eigenvalues correspond to the zeros of the Riemann zeta function, is analyzed using Fourier and WKB analysis. The Fourier analysis leads…

We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the…