Runbo Li

collaborators

15 papers

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

Primes in arithmetic progressions to smooth moduli: A minorant version

Runbo Li

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

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

On prime-producing sieves and distribution of $I^\pm p - I^^{2}$ mod $1$

Runbo Li

The author proves that there are infinitely many primes $p$ such that $∥ I^\pm p - I^^{2} ∥ < p^{- \frac{28}{87}}$ , where $I^\pm$ is an irrational number and $I^^{2}$ is a real number. This sharp…

math.NT2025

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 $[x - x^{I^} ¸, x]$ for some $0.52 ⩽ I^¸ ⩽ 0.525$ , showing that the interval $…

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

On the largest prime factor of integers in short intervals III

Primes in arithmetic progressions to smooth moduli: A minorant version

Largest square divisors of shifted primes

On prime-producing sieves and distribution of I^±p−I^2 mod 1

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

On prime-producing sieves and distribution of $I^\pm p - I^^{2}$ mod $1$