Related papers: Asymptotic Large Sieve
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
We complement the argument of M. Z. Garaev (2009) with several other ideas to obtain a stronger version of the large sieve inequality with sparse exponential sequences of the form $\lambda^{s_n}$. In particular, we obtain a result which is…
We evaluate the asymptotic size of various sums of G\'al type, in particular $$S( \mathcal{M}):=\sum_{m,n\in\mathcal{M}} \sqrt{(m,n) \over [m,n]},$$ where $\mathcal{M}$ is a finite set of integers. Elaborating on methods recently developed…
We determine the general form of the asymptotics for Dirichlet eigenvalues of the one-dimensional linear damped wave operator. As a consequence, we obtain that given a spectrum corresponding to a constant damping term this determines the…
We establish the short-time asymptotic behaviour of the Markovian semigroups associated with strongly local Dirichlet forms under very general hypotheses. Our results apply to a wide class of strongly elliptic, subelliptic and degenerate…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
We establish some asymptotic expansions for infinite weighted convolutions of distributions having light subexponential tails. Examples are presented, some showing that in order to obtain an expansion with two significant terms, one needs…
We study the first moment of primitive quadratic Dirichlet $L$-functions. Assuming the Riemann hypothesis and the generalized Lindel\"of hypothesis, we obtain an asymptotic formula at the central point with error $O(X^{1/4+\epsilon})$, and…
In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
We prove an asymptotic formula for the number of integers $\leq x$ which can be written as the product of $k ~(\geq 2)$ distinct primes $p_1\cdots p_k$ with each prime factor in an arithmetic progression $p_j\equiv a_j \bmod q$, $(a_j,…
We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general…
In this paper we address the problem of computing asymptotic formulae for the expected values and second moments of central values of primitive Dirichlet $L$-functions $L(1/2,\chi_{8d}\otimes\psi)$ when $\psi$ is a fixed even primitive…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
We describe the asymptotic behaviour and the dependence on the regularization of logarithmically divergent integrals of products of meromorphic and antimeromorphic forms on complex manifolds. Our formula is expressed in terms of residues of…
Asymptotic expansions are obtained for contour integrals of the form \[ \int_a^b \exp \left( - zp(t) + z^{\nu /\mu } r(t) \right)q(t)dt, \] in which $z$ is a large real or complex parameter, $p(t)$, $q(t)$ and $r(t)$ are analytic functions…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
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 give an elementary algebraic proof of some asymptotic estimates (called by Demailly asymptotic Morse inequalities) for the dimensions of cohomology groups of the difference of two ample line bundles on a smooth complex projective variety…