Runbo Li

collaborators

8 papers

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…

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 the exceptional set in the $ab c$ conjecture