Junren Zheng

collaborators

3 papers

math.NT2026

Mixed incomplete character sums of rational functions with smooth moduli

Todd Cochrane, Andrew Granville, Junren Zheng

Let $I ¨ = I ¨ _{q}$ be a primitive character mod $q$ and fix $I^ > 0$ . In 1989 Graham and Ringrose gave strong bounds on character sums $\sum_{M < n \leq M + N} I ¨ (n)$ in intervals of length $N…

math.NT2025

On the Brun--Titchmarsh theorem. I

Ping Xi, Junren Zheng

The classical Brun--Titchmarsh theorem gives an upper bound, which is of correct order of magnitude in the full range, for the number of primes $p ⩽ x$ satisfying $p\equiv a…

math.NT2025

On the Brun--Titchmarsh theorem. II

Ping Xi, Junren Zheng

Denote by $I ¨ (x; q, a)$ the number of primes $p ⩽ x$ with $p \equiv a mod q .$ We prove new upper bounds for $I ¨ (x; q, a)$ when $q$ is a large prime very close to $x$ , imp…