Ping Xi

collaborators

3 papers

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…

math.NT2025

Estimates for trilinear and quadrilinear character sums

Ãtienne Fouvry, Igor E. Shparlinski, Ping Xi

We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new…