Runbo Li

activity

20232026

most citedPrimes in almost all short intervals

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

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7 papers · 1 filter

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…

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

On the exceptional set in the $ab c$ conjecture

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