Csaba Sándor

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20172020

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8 papers · 1 filter

math.NT2020

Additive representation functions and discrete convolutions

Csaba Sándor

For a set $A$ of non-negative integers, let $R_{A} (n)$ denote the number of solutions to the equation $n = a + a^{'}$ with $a$ , $a^{'} \in A$ . Denote by $χ_{A} (n)$ the characteristic function of…

math.NT2020

Generalized Sidon sets of perfect powers

Sandor Kiss, Csaba Sandor

For $h \geq 2$ and an infinite set of positive integers $A$ , let $R_{A, h} (n)$ denote the number of solutions of the equation $a_{1} + a_{2} + \dots{} + a_{h} = n, a_{1} \in A, \dots…

math.NT2019

A note on the lower bound of representation functions

Xing-Wang Jiang, Csaba Sandor, Quan-Hui Yang

For a set $A$ of nonnegative integers, let $R_{2} (A, n)$ denote the number of solutions to $n = a + a^{'}$ with $a, a^{'} \in A$ , $a < a^{'}$ . Let $A_{0}$ be the Thue-Morse sequence and $B_0=\mathbb{N}\…

math.NT2019

On the values of representation functions II

Xing-Wang Jiang, Csaba Sandor, Quan-Hui Yang

For a set $A$ of nonnegative integers, let $R_{2} (A, n)$ and $R_{3} (A, n)$ denote the number of solutions to $n = a + a^{'}$ with $a, a^{'} \in A$ , $a < a^{'}$ and $a \leq a^{'}$ , respectively. In this paper…

math.NT2018

Generalizations of some results about the regularity properties of an additive representation function

Sándor Z. Kiss, Csaba Sándor

Let $A = {a_{1}, a_{2}, \dots}$ $(a_{1} < a_{2} < \dots)$ be an infinite sequence of nonnegative integers, and let $R_{A, 2} (n)$ denote the number of solutions of $a_{x}+a_{y}=n…

math.NT2017

On infinite multiplicative Sidon sets

Péter Pál Pach, Csaba Sándor

We prove that if $A$ is an infinite multiplicative Sidon set, then $n \to \infty lim inf \frac{∣ A ( n ) ∣ - π ( n )}{\frac{n ^{3/4}}{( l o g n ) ^{3}}} < \infty$ and construct an infinite mul…