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Asymptotic integration theory gives a collection of results which provide a thorough description of the asymptotic growth and zero distribution of solutions of (*) $f''+P(z)f=~0$, where $P(z)$ is a polynomial. These results have been used…

Complex Variables · Mathematics 2020-08-25 Gary G. Gundersen , Janne Heittokangas , Amine Zemirni

In the 70's Igusa developed a uniform theory for local zeta functions and oscillatory integrals attached to polynomials with coefficients in a local field of characteristic zero. In the present article this theory is extended to the case of…

Number Theory · Mathematics 2015-10-14 Willem Veys , W. A. Zuniga-Galindo

By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of…

Classical Analysis and ODEs · Mathematics 2018-11-09 Konstantinos Kalimeris , Athanassios S. Fokas

We provide an asymptotic expansion for $\sum_{k=1}^n \left\{\sqrt{k}\right\}$. In the same spirit, we discuss the case of n-th root and it relation to special values of Riemman's zeta function.

Classical Analysis and ODEs · Mathematics 2017-06-13 Haroun Meghaichi

The omega limit sets plays a fundamental role to construct global attractors for topological semi-dynamical systems with continuous time or discrete time. Therefore, it is important to know when omega limit sets become nonempty compact…

General Topology · Mathematics 2021-09-24 Junya Nishiguchi

We prove that a (globally) subanalytic p-adic function which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken…

Algebraic Geometry · Mathematics 2011-01-28 R. Cluckers , G. Comte , F. Loeser

We give an informal introduction to the most basic techniques used to evaluate moments on the critical line of the Riemann zeta-function and to find asymptotics for sums of arithmetic functions.

Number Theory · Mathematics 2007-05-23 David W. Farmer

In this paper, we study the asymptotic behavior of least energy nodal solutions $u_p(x)$ to the following fourth-order elliptic problem \[ \begin{cases} \Delta^2 u =|u|^{p-1}u \quad &\hbox{in}\;\Omega, \\ u=\frac{\partial u}{\partial \nu}=0…

Analysis of PDEs · Mathematics 2023-06-08 Zhijie Chen , Zetao Cheng , Hanqing Zhao

We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…

Analysis of PDEs · Mathematics 2021-10-12 Michela Eleuteri , Luca Lussardi , Andrea Torricelli

We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show that the extension provides a method of finding singularities of solutions of nonlinear differential equations, using…

Classical Analysis and ODEs · Mathematics 2016-09-07 Ovidiu Costin

We consider the fragmentation at nodes of the L\'{e}vy continuous random tree introduced in a previous paper. In this framework we compute the asymptotic for the number of small fragments at time $\theta$. This limit is increasing in…

Probability · Mathematics 2007-05-23 Romain Abraham , Jean-François Delmas

Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main…

Group Theory · Mathematics 2017-03-02 Steffen Kionke

We introduce p-equivalence by asymptotic probabilities, which is a weak almost-equivalence based on zero-one laws in finite model theory. In this paper, we consider the computational complexities of p-equivalence problems for regular…

Formal Languages and Automata Theory · Computer Science 2016-09-15 Yoshiki Nakamura

We analyse a collection of mixed moments of the Riemann zeta function and establish the validity of asymptotic formulae. Such examinations are performed both unconditionally and under the assumption of a weaker version of the $abc$…

Number Theory · Mathematics 2022-10-28 Javier Pliego

In this paper we introduce the concept of O-asymptotic classes of finite structures, melding ideas coming from 1-dimensional asymptotic classes and o-minimality. The results we present here include a cell-decomposition result for…

Logic · Mathematics 2020-01-01 Darío García

We construct the p-adic zeta function for a one-dimensional (as a p-adic Lie extension) non-commutative p-extension of a totally real number field such that the finite part of its Galois group is a pgroup with exponent p. We first calculate…

Number Theory · Mathematics 2019-12-19 Takashi Hara

We introduce a new representation for the rescaled Appell polynomials and use it to obtain asymptotic expansions to arbitrary order. This representation consists of a finite sum and an integral over a universal contour (i.e. independent of…

Classical Analysis and ODEs · Mathematics 2019-11-19 J. Fernando Barbero G , Jesús Salas , Eduardo J. S. Villaseñor

In this article we study asymptotic properties of certain discrete groups $\Gamma$ acting by isometries on a product $\XX=\XX_1\times \XX_2$ of locally compact Hadamard spaces. The motivation comes from the fact that Kac-Moody groups over…

Metric Geometry · Mathematics 2014-11-11 Gabriele Link

We propose a refined version of the existing conjectural asymptotic formula for the moments of the family of quadratic Dirichlet L-functions over rational function fields. Our prediction is motivated by two natural conjectures that provide…

Number Theory · Mathematics 2020-09-01 Adrian Diaconu , Henry Twiss

We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…

Combinatorics · Mathematics 2024-05-15 Torin Greenwood , Tristan Larson