Ping Xi

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20242026

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5 papers · 1 filter

math.NT2026

Short sums of the Möbius function over function fields

Etienne Fouvry, Igor E. Shparlinski, Ping Xi

We develop a new method which allows us to estimate, with a power saving, sums of the M{ö}bius function over function fields $F_{p} (X)$ . The sums run over monic polynomials…

math.NT2026

Tridimensional character sums with polynomial arguments and applications

Étienne Fouvry, Igor E. Shparlinski, Ping Xi

Let $p$ be a large prime and $χ$ a non-trivial Dirichlet character modulo $p$ . We study the character sum \[ \sum_{a \sim A} \sum_{b \sim B} \sum_{c \sim C} α(a,b) β(c)χ(f(a) + bc)…

math.NT2025

On the Brun--Titchmarsh theorem. II

Ping Xi, Junren Zheng

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

math.NT2024

Estimates for trilinear and quadrilinear character sums

Étienne 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…

math.NT2024

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…