Runbo Li

activity

20232026

most citedPrimes in almost all short intervals

2 citations · 4 across the 17 of their papers we have counts for

collaborators

20 papers

math.NT2026

Large value estimates for Dirichlet polynomials and trilinear sums over short intervals

Runbo Li

Recently, Matomäki, Pandey, Pliego, Teräväinen and Wang improved the Baker--Harman--Pintz estimate of trilinear sums over short intervals of length $x^{θ}$ , which naturally reduces t…

math.NT2026

Primes in arithmetic progressions to large moduli and refinements of Harman's sieve

Runbo Li

We study the average distribution of primes of size $x$ in arithmetic progressions to moduli larger than $x^{\frac{1}{2}}$ . Using arithmetic information from the works of many auth…

math.NT2026

On the largest prime factor of integers in short intervals III

Runbo Li

Using Watt's mean value theorem and a delicate sieve decomposition, the author shows that the interval $[x, x + x^{\frac{1}{2} + ε}]$ contains an integer with a prime factor…

math.NT2025

An average Brun-Titchmarsh theorem and shifted primes with a large prime factor

Runbo Li

The author studies an average version of Brun-Titchmarsh theorem with large moduli. Using Maynard's recent breakthrough on the Bombieri-Friedlander-Iwaniec type triple convolution…

math.NT2025

On the exceptional set in the $ab c$ conjecture

Runbo Li

The $ab c$ conjecture states that there are only finitely many triples of coprime positive integers $(a, b, c)$ such that $a + b = c$ and $rad (ab c) < c^{1 - ε}$ for any $ε> 0…

math.NT2025

On almost primes in Piatetski-Shapiro sequences

Runbo Li

The author proves that for $0.9985 < γ < 1$ , there exist infinitely many primes $p$ such that $[p^{1/ γ}]$ has at most 5 prime factors counted with multiplicity. This gives an improv…

math.NT2025

Largest square divisors of shifted primes

Runbo Li

The author shows that there are infinitely many primes $p$ such that for any nonzero integer $a$ , $p - a$ is divisible by a square $d^{2} > p^{\frac{1}{2} + \frac{1}{700}}$ . The exponent…

math.NT2025

Primes in arithmetic progressions to smooth moduli: A minorant version

Runbo Li

The author prove that there exists a function $ρ (n)$ which is a minorant for the prime indicator function $1_{p} (n)$ and has distribution level $\frac{10}{19}$ in arithmet…

math.NT2025

On prime-producing sieves and distribution of $α p - β$ mod $1$

Runbo Li

The author proves that there are infinitely many primes $p$ such that $∥ α p - β ∥ < p^{- \frac{28}{87}}$ , where $α$ is an irrational number and $β$ is a real number. This sharpens…

math.NT2025

A note on variants of Buchstab's identity

Runbo Li

The author proves variants of Buchstab's identity on sieve functions, refining the previous work on new iteration rules of Brady. The main tool used in the proof is a special form…

math.NT2024★ 2 cited

Primes in almost all short intervals

Runbo Li

The author sharpens a result of Jia (1996), showing that the interval $[n, n + n^{\frac{1}{21.5} + ε}]$ contains prime numbers for almost all $n$ . Watt's mean value bound, a…

math.NT2024

On the largest prime factor of quadratic polynomials

Runbo Li

Let $x$ denote a sufficiently large integer. We show that the recent result of Grimmelt and Merikoski actually yields the largest prime factor of $n^{2} + 1$ is greater than $x^{1.317…

math.NT2024

On Chen's theorem, Goldbach's conjecture and almost prime twins II

Runbo Li

Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1, 2} (N)$ as the number of primes $p$ that such that $N - p$ has at most…

math.GM2024

A remark on large even integers of the form $p + P_{3}$

Runbo Li

Let $N$ denotes a sufficiently large even integer, $p$ denotes a prime and $P_{r}$ denotes an integer with at most $r$ prime factors. In this paper, we study the solutions of the e…

math.NT2024

Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals

Runbo Li

We provide a new hybrid estimation of single exponential sums, combining Van der Corput, Huxley and Bourgain's result. We also focus on primes in short intervals $(x - x^{α}, x]$ under…

math.NT2024

A remark on the distribution of $p$ modulo one involving primes of special type II

Runbo Li

Let $P_{r}$ denote an integer with at most $r$ prime factors counted with multiplicity. In this paper we prove that for some $λ < \frac{1}{12}$ , the inequality ${p} < p^{- λ}$ …

math.NT2024

On the upper and lower bound orders of almost prime triples

Runbo Li

A Hardy-Littlewood triple is a 3-tuple of integers with the form $(n, n + 2, n + 6)$ . In this paper, we study Hardy-Littlewood triples of the form $(p, P_{a}, P_{b})$ and improve the u…

math.NT2023

Remarks on additive representations of natural numbers

Runbo Li

For two relatively prime square-free positive integers $a$ and $b$ , we study integers of the form $a p + b P_{2}$ and give a new lower bound for the number of such representations, w…

math.NT2023

On some problems of primes with the floor function

Runbo Li

Let $[x]$ be the largest integer not exceeding $x$ . For $0 < θ \leq 1$ , let $π_{θ} (x)$ denote the number of integers $n$ with $1 \leq n \leq x^{θ}$ such that $\left[\frac{x}{n}…

math.NT2023★ 2 cited

The number of primes in short intervals and numerical calculations for Harman's sieve

Runbo Li

The author gives nontrivial upper and lower bounds for the number of primes in the interval $[x - x^{θ}, x]$ for some $0.52 ⩽ θ ⩽ 0.525$ , showing that the interval $[x…

Large value estimates for Dirichlet polynomials and trilinear sums over short intervals

Primes in arithmetic progressions to large moduli and refinements of Harman's sieve

On the largest prime factor of integers in short intervals III

An average Brun-Titchmarsh theorem and shifted primes with a large prime factor

On the exceptional set in the abc conjecture

On almost primes in Piatetski-Shapiro sequences

Largest square divisors of shifted primes

Primes in arithmetic progressions to smooth moduli: A minorant version

On prime-producing sieves and distribution of αp−β mod 1

A note on variants of Buchstab's identity

Primes in almost all short intervals

On the largest prime factor of quadratic polynomials

On Chen's theorem, Goldbach's conjecture and almost prime twins II

A remark on large even integers of the form p+P3​

Hybrid estimation of single exponential sums, exceptional characters and primes in short intervals

A remark on the distribution of p​ modulo one involving primes of special type II

On the upper and lower bound orders of almost prime triples

Remarks on additive representations of natural numbers

On some problems of primes with the floor function

The number of primes in short intervals and numerical calculations for Harman's sieve

On the exceptional set in the $ab c$ conjecture

On prime-producing sieves and distribution of $α p - β$ mod $1$

A remark on large even integers of the form $p + P_{3}$

A remark on the distribution of $p$ modulo one involving primes of special type II