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

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7 papers · 2 filters

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…

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

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