## 12 Citations

### PARTITIONS INTO PRIME POWERS

- Mathematics
- 2021

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

- Mathematics
- 2020

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

- MathematicsTaiwanese Journal of 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…

### What is an answer? - remarks, results and problems on PIO formulas in combinatorial enumeration, part I

- Mathematics, Computer Science
- 2018

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

- MathematicsIndagationes Mathematicae
- 2020

### Adversarial Erasing Attention for Person Re-Identification in Camera Networks Under Complex Environments

- Computer ScienceIEEE Access
- 2020

A novel person Re-ID method named Adversarial Erasing Attention (AEA) to mine discriminative completed features using an adversarial way and combine the features learned from the basic and complementary networks to represent the pedestrian image.

## References

SHOWING 1-10 OF 19 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

- MathematicsMathematische 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

- Mathematics
- 1997

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

- Mathematics
- 2008

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…

### on Hardy-Littlewood Circle Method

- Mathematics
- 2010

The proof of Roth’s Theorem on sets with no three-term arithmetic progressions can be placed in a general framework of estimates of exponential sums and diophantine approximation called the…

### Introduction to analytic number theory

- Mathematics
- 1976

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

- Mathematics
- 2009

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…