# Polynomial Partition Asymptotics

@article{Dunn2017PolynomialPA,
title={Polynomial Partition Asymptotics},
author={Alexander Dunn and Nicolas Robles},
journal={arXiv: Number Theory},
year={2017}
}
• Published 30 April 2017
• Mathematics
• arXiv: Number Theory
Note on partitions into polynomials with number of parts in an arithmetic progression
Let $k, a\in \mathbb{N}$ and let $f(x)\in\mathbb{Q}[x]$ be a polynomial with degree ${\rm deg}(f)\ge 1$ such that all elements of the sequence $\{f(n)\}_{n\in\mathbb{N}}$ lies on $\mathbb{N}$ and
PARTITIONS INTO PRIME POWERS
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
Partitions into prime powers and other restricted partition functions
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
Counting the Number of Solutions to Certain Infinite Diophantine Equations
• Mathematics
• 2019
Let $r, n$ be positive integers. In this paper, we prove a generating function and an asymptotic formula for the number solutions of the following infinite Diophantine equation: $$n=1^{r}\cdot Random permutations with logarithmic cycle weights • Mathematics • 2018 We consider random permutations on \Sn with logarithmic growing cycles weights and study the asymptotic behavior as the length n tends to infinity. We show that the cycle count process converges Power partitions and saddle-point method • Mathematics Journal of Number Theory • 2019 What is an answer? - remarks, results and problems on PIO formulas in combinatorial enumeration, part I It is proved here that every linear recurrence sequence of integers has an effective formula in the sense of being closed in the authors' sense. Partitions into Piatetski-Shapiro sequences • Mathematics • 2021 Let κ be a positive real number and m ∈ N ∪ {∞} be given. Let pκ,m(n) denote the number of partitions of n into the parts from the Piatestki-Shapiro sequence (⌊l⌋)l∈N with at most m times (repetition The saddle-point method for general partition functions • Mathematics Indagationes Mathematicae • 2020 ## References SHOWING 1-10 OF 21 REFERENCES On the Asymptotic Behaviour of General Partition Functions, II • Mathematics • 2003 AbstractLet$$\mathcal{A}$$= {a1, a2,...} be a set of positive integers and let p$$\mathcal{A}$$(n) and q$$\mathcal{A} (n) denote the number of partitions of n into a's, resp. distinct a's.
Partitions into kth powers of terms in an arithmetic progression
• Mathematics
Mathematische Zeitschrift
• 2018
G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a similar asymptotic formula for the number of partitions
On exponential sums
Let f be a polinomial with coefficients in a finite field F. Let $\Psi : F \to C^{\ast}$ be a non-trivial additive character. In this paper we give bounds for the exponential sums \$\sum_{x\in F^n}
On the Asymptotic Behaviour of General Partition Functions
• Mathematics
• 2000
AbstractFor A = {a1, a2,...} ⊂ N, let pA(n) denote the number of partitions of n into a's and let qA(n) denote the number of partitions of n into distinct a's. The asymptotic behaviour of the
On the number of partitions into primes
Abstract There is, apparently, a persistent belief that in the current state of knowledge it is not possible to obtain an asymptotic formula for the number of partitions of a number n into primes
Introduction to analytic number theory
This is the first volume of a two-volume textbook which evolved from a course (Mathematics 160) offered at the California Institute of Technology during the last 25 years. It provides an introduction
The Hardy—Littlewood circle method
One of the most significant all-purpose tools available in the study of rational points on higher-dimensional algebraic varieties is the Hardy—Littlewood circle method. In this chapter we will
Zeta-Functions Defined by Two Polynomials
• Mathematics, Philosophy
• 2002
The analytic continuation of certain multiple zeta-functions is shown. In particular, the analytic continuation of the zeta-function ζ(s; P, Q), defined by two polynomials P and Q, follows. Then the
Tables of Mellin Transforms
I. Mellin Transforms.- Some Applications of the Mellin Transform Analysis.- 1.1 General Formulas.- 1.2 Algebraic Functions and Powers of Arbitrary Order.- 1.3 Exponential Functions.- 1.4 Logarithmic