Yu-Chen Sun

activity

20172026

most citedSolutions to some sign change problems on the functions involving sums of divisors

1 citations · 2 across the 14 of their papers we have counts for

collaborators

16 papers

math.NT2026

The optimal scale in Linnik's microsquare problem for almost all integers

Yu-Chen Sun, Lilu Zhao

We prove that, for any positive function $Ψ (t) \to \infty$ , almost all positive integers $n$ satisfying $4 ∤ n$ and $n \neq \equiv 7 (mod 8)$ can be written as $n = x^{2} + y^{2} + z^{2}$ , where $…

math.NT2026

An improved upper bound on the Ruzsa number

Yuchen Ding, Yu-Chen Sun, Lilu Zhao

Let $R_{m}$ be the least positive integer $r$ such that there exists a set $A \subseteq Z_{m}$ with $A + A = Z_{m}$ for which the number of ordered solutions of $n = x + y$ wi…

math.NT2026

An improved lower bound for odd integers not of the form $p + 2^{a} + 2^{b}$

Yuchen Ding, Yu-Chen Sun, Lilu Zhao

Let $x$ be sufficiently large and \[ N(x)=\big|\bigl\{n\le x:n\ \text{is odd and }n\ne p+2^a+2^b \textrm{ with } p \text{ a prime and } a,b\in \mathbb{N}\bigr\}\big|. \] Motivated…

math.NT2026

Representations of positive integers by three almost-prime squares

Yue-Feng She, Yu-Chen Sun, Guang-Liang Zhou

Let $P_{r}$ denote an integer with at most $r$ prime factors, counted with multiplicity. It is known that every sufficiently large integer $N$ satisfying $N \equiv 3 (mod 24)$ and $…

math.NT2026

Linear equations in Piatetski-Shapiro primes

Xuancheng Shao, Yu-Chen Sun

We establish discorrelation estimates between the Piatetski-Shapiro prime set \[ \mathcal{P}_γ := \{p \text{ is prime and } p = \lfloor n^{1/γ} \rfloor \text{ for some } n \in \mat…

math.NT2026

Small values of signed harmonic sums and logarithmic means of multiplicative functions

Oleksiy Klurman, Marc Munsch, Yu-Chen Sun

We construct sequences ${a_{n}}_{n \in N} \in {- 1, 1}^{N}$ with small values of signed harmonic sums \[ \sum_{n\in\mathcal{A}\cap[1,N]}\frac{a_n}{n}, \] for any reas…

math.NT2026

Large sieve inequality for sums of Legendre symbols over short intervals

Marc Munsch, Igor Shparlinski, Yu-Chen Sun +1

Using the Burgess bound and the Selberg sieve, we obtain an upper bound for the second moment of sums of Legendre symbols over intervals , with the modulus ranging over primes . Th…

math.NT2025

Cross representations of additive complements of $r$ -th powers

Yuchen Ding, Ben Krause, Csaba Sándor +2

Let $N$ be the set of natural numbers and $S_{r} = {1^{r}, 2^{r}, 3^{r}, \dots}$ the set of $r$ -th powers, where $r \geq 2$ is a natural number. Let $\mathcal{W}_r…

math.NT2025

Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems

Yuchen Ding, Christian Elsholtz, Yu-Chen Sun

In this note, we discuss two problems of Sárközy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.

math.NT2024★ 1 cited

Solutions to some sign change problems on the functions involving sums of divisors

Yuchen Ding, Hao Pan, Yu--Chen Sun

In this note, we solve some sign change problems on the functions involving sums of divisors posed by Pongsriiam recently.

math.NT2022

A note on additive complements of the squares

Yuchen Ding, Yu-Chen Sun, Li-Yuan Wang +1

Let $S = {1^{2}, 2^{2}, 3^{2}, ...}$ be the set of squares and $W = {w_{n}}_{n = 1}^{\infty} \subset N$ be an additive complement of $S$ so that $\mathcal…

math.NT2019★ 1 cited

Vinogradov three prime theorem with Piatetski-Shapiro primes

Yu-Chen Sun, Shanshan Du, Hao Pan

We prove that, for any $c_{1}, c_{2}, c_{3} \in (1, 41/35)$ , every sufficiently large odd number $N$ can be represented as the sum of three primes $N = p_{1} + p_{2} + p_{3}$ such that $p_i = \lfloo…

math.CO2019

A $q$ -analogue of Wilson's congruence

Hao Pan, Yu-Chen Sun

Let $C_{n}$ be the set of all permutation cycles of length $n$ over ${1, 2, \dots, n}$ . Let $f_{n} (q) := σ \in C_{n + 1} \sum q^{m aj σ}$ be a…

math.NT2018

A note on the sum of reciprocals

Yuchen Ding, Yu-Chen Sun

For a fixed positive integer $m$ and any partition $m = m_{1} + m_{2} + \dots + m_{e}$ , there exists a sequence ${n_{i}}_{i = 1}^{k}$ of positive integers such that $$m=\frac{1}{n_{1}}…

math.NT2018

On the gaps between consecutive primes

Yu-Chen Sun, Hao Pan

Let $p_{n}$ denote the $n$ -th prime. For any $m \geq 1$ , there exist infinitely many $n$ such that $p_{n} - p_{n - m} \leq C_{m}$ for some large constant $C_{m} > 0$ , and $$p_{n+1}-p_n\geq \frac…

math.NT2017

The Green-Tao theorem for primes of the form $x^{2} + y^{2} + 1$

Yu-Chen Sun, Hao Pan

We prove that the primes of the form $x^{2} + y^{2} + 1$ contain arbitrarily long non-trivial arithmetic progressions.

The optimal scale in Linnik's microsquare problem for almost all integers

An improved upper bound on the Ruzsa number

An improved lower bound for odd integers not of the form p+2a+2b

Representations of positive integers by three almost-prime squares

Linear equations in Piatetski-Shapiro primes

Small values of signed harmonic sums and logarithmic means of multiplicative functions

Large sieve inequality for sums of Legendre symbols over short intervals

Cross representations of additive complements of r-th powers

Problems 66 and 67 on sums of residue classes and primes of András Sárközy's collection of unsolved problems

Solutions to some sign change problems on the functions involving sums of divisors

A note on additive complements of the squares

Vinogradov three prime theorem with Piatetski-Shapiro primes

A q-analogue of Wilson's congruence

A note on the sum of reciprocals

On the gaps between consecutive primes

The Green-Tao theorem for primes of the form x2+y2+1

An improved lower bound for odd integers not of the form $p + 2^{a} + 2^{b}$

Cross representations of additive complements of $r$ -th powers

A $q$ -analogue of Wilson's congruence

The Green-Tao theorem for primes of the form $x^{2} + y^{2} + 1$