Related papers: Asymptotics of generalized partial theta functions…

In this note we define L-functions of finite graphs and study the particular case of finite cycles in the spirit of a previous paper that studied spectral zeta functions of graphs. The main result is a suggestive equivalence between an…

We consider a generalized Mathieu series where the summands of the classical Mathieu series are multiplied by powers of a complex number. The Mellin transform of this series can be expressed by the polylogarithm or the Hurwitz zeta…

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…

In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…

We study the precise asymptotic behavior of a non-trivial solution that converges to zero, as time tends to infinity, of dissipative systems of nonlinear ordinary differential equations. The nonlinear term of the equations may not possess a…

Bessel and modified Bessel functions of imaginary order $i\nu$ ($\nu >0$) are studied. Asymptotic expansions are derived as $\nu \to \infty$ that are uniformly valid in unbounded complex domains, with error bounds provided. Coupled with…

Let $P$ be a symmetric $2a$-order classical strongly elliptic pseudodifferential operator with even symbol $p(x,\xi )$ on $R^n$ ($0<a<1$), for example a perturbation of $(-\Delta )^a$. Let $\Omega \subset R^n$ be bounded, and let $P_D$ be…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

For a complex variable $s$ and real parameters $a$ and $\lambda$ with $a>0$, let $\phi(s,a,\lambda)$ denote the Lerch zeta-function with a complex variable, $\phi^{\ast}(s,a,\lambda)$ a slight modification of $\phi(s,a,\lambda)$ defined by…

Uniform asymptotic expansions are derived for reverse generalised Bessel polynomials of large degree $n$, real parameter $a$, and complex argument $z$, which are simpler than previously known results. The defining differential equation is…

We describe in detail three distinct families of generalized zeta functions built over the (nontrivial) zeros of a rather general arithmetic zeta or L-function, extending the scope of two earlier works that treated the Riemann zeros only.…

We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $\Delta_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in…

We prove an asymptotic formula for the eighth moment of Dirichlet $L$-functions averaged over primitive characters $\chi$ modulo $q$, over all moduli $q\leq Q$ and with a short average on the critical line. Previously the same result was…

We establish asymptotic estimates of Mathieu-type series defined by sequences with power-logarithmic or factorial behavior. By taking the Mellin transform, the problem is mapped to the singular behavior of certain Dirichlet series, which is…

Due to their singularities, multiple zeta functions behave sensitively at non-positive integer points. In this article, we focus on the asymptotic behavior at the origin $(0,\dots, 0)$ and unveil the generating series of the asymptotic…

In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then…

In this article, we obtain the analytic continuation of the multiple shifted Lucas zeta function, multiple Lucas $L$-function associated to Dirichlet characters and additive characters. We then compute a complete list of exact singularities…

This paper is concerned with the asymptotic expansions of the amplitude of the solution of the Helmholtz equation. The original expansions were obtained using a pseudo-differential decomposition of the Dirichlet to Neumann operator. This…

We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of the Watson lemma recently proved elsewhere, we discuss a large class of functions determined by the same…