Related papers: On asymptotics for lacunary partition functions

Here we examine the number of ways to partition an integer $n$ into $k$th powers when $n$ is large. Simplified proofs of some asymptotic results of Wright are given using the saddle-point method, including exact formulas for the expansion…

We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of…

We present a prototype for Wilsonian analysis of asymptotics of supersymmetric partition functions of non-abelian gauge theories. Localization allows expressing such partition functions as an integral over a BPS moduli space. When the limit…

We present a sufficient condition of existence of asymptotic expansion in negative power series for a function defined by Taylor series and unitary formulas for coefficients of this expansion. An example of computing scheme for arctangent…

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…

We determine the asymptotic behaviour of certain incomplete Betafunctions.

For a subset $\mathcal A\subset \mathbb N$, let $p_{\mathcal A}(n)$ denote the restricted partition function which counts partitions of $n$ with all parts lying in $\mathcal A$. In this paper, we use a variation of the Hardy-Littlewood…

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…

New algorithms for computing of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes are presented. The algorithms are based on special techniques of sequential phase space reduction, which can…

Assuming the asymptotic character of divergent perturbation series, we address the problem of ambiguity of a function determined by an asymptotic power expansion. We consider functions represented by an integral of the Laplace-Borel type,…

The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.

Let $p_n$ be the number of partitions of an integer $n$. For each of the partition statistics of counting their parts, ranks, or cranks, there is a natural family of integer polynomials. We investigate their asymptotics and the limiting…

In this paper, we study the asymptotic behavior of radial solutions for several weighted elliptic equations with power type or exponential type nonlinearities on an annulus.

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…

We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…

We introduce the notion of asymptotic partition regularity for Diophantine equations. We show how this notion is at the core of almost all known negative results in the Ramsey theory of equations, and we use it to produce new ones, as in…

We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated…

In this paper, we study asymptotics of the thermal partition function of a model of quantum mechanical fermions with matrix-like index structure and quartic interactions. This partition function is given explicitly by a Wronskian of the…

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.

We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For non-zero coupling, the corresponding multi-variable partition functions can be written in terms of…