Ping Xi

activity

20092026

most citedQuadratic polynomials at prime arguments

6 citations · 19 across the 21 of their papers we have counts for

collaborators

23 papers

math.NT2026

Horizontal moments of Kloosterman sums and a density version of sieves

Ping Xi

Denote by $Kl (a, n)$ the normalized Kloosterman sum modulo $n$ . In this paper, we study the moments of $∣ Kl (1, n) ∣$ on average over $n ⩽ X$ , and show that \b…

math.NT2023

A uniform Weyl bound for L-functions of Hilbert modular forms

Han Wu, Ping Xi

We establish a Weyl-type subconvexity of $L (\frac{1}{2}, f)$ for spherical Hilbert newforms $f$ with level ideal $N^{2}$ , in which $N$ is required to be cube-fr…

math.NT2023

A double character sum of Conrey-Iwaniec and Petrow-Young

Ping Xi

We show that a double character sum, appearing in the work of Conrey-Iwaniec and Petrow-Young on Weyl bound for certain $L$ -functions, is essentially a hypergeometric sum introduce…

math.NT2022

Bilinear forms with trace functions over arbitrary sets, and applications to Sato-Tate

Ping Xi

We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be arbitrary subsets in $\mathbf{F}_…

math.NT2022

Bounds on bilinear forms with Kloosterman sums

Bryce Kerr, Igor E. Shparlinski, Xiaosheng Wu +1

We prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by É. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, É. Fouvry,…

math.NT2022★ 1 cited

A conjecture of Sárközy on quadratic residues, II

Yong-Gao Chen, Ping Xi

Denote by $R_{p}$ the set of all quadratic residues in $F_{p}$ for each prime $p$ . A conjecture of A. Sárközy asserts, for all sufficiently large $p$ , that no subset…

math.NT2021★ 1 cited

Lang--Trotter Conjecture for CM Elliptic Curves

Daqing Wan, Ping Xi

Given an elliptic curve $E$ over $Q$ and non-zero integer $r$ , the Lang--Trotter conjecture predicts a striking asymptotic formula for the number of good primes $p\leqslan…

math.NT2021

Moments and equidistributions of multiplicative analogues of Kloosterman sums

Ping Xi

We consider a family of character sums as multiplicative analogues of Kloosterman sums. Using Gauss sums, Jacobi sums and Deligne's bound for hyper-Kloosterman sums, we establish a…

math.NT2021

Addendum to "Arithmetic exponent pairs of algebraic trace functions and applications"

Jie Wu, Ping Xi

This addendum devotes to a detailed proof for the inequality (9.14) in our joint work: Arithmetic exponent pairs for algebraic trace functions and applications, with an appendix by…

math.NT2018

Equidistributions of Jacobi sums

Ping Xi

Let $F_{q}$ be a finite field of $q$ elements. We show that the normalized Jacobi sum $J (χ, η) / q$ , for each fixed non-trivial multiplicative character $η$ , becomes equ…

math.NT2018

When Kloosterman sums meet Hecke eigenvalues

Ping Xi

By elaborating a two-dimensional Selberg sieve with asymptotics and equidistributions of Kloosterman sums from $ℓ$ -adic cohomology, as well as a Bombieri--Vinogradov type mean v…

math.NT2017★ 6 cited

Counting fundamental solutions to the Pell equation with prescribed size

Ping Xi

The cardinality of the set of $D ⩽ x$ for which the fundamental solution of the Pell equation $t^{2} - D u^{2} = 1$ is less than $D^{\frac{1}{2} + α}$ with $α \in [\frac{1}{2}, 1]$ is stu…

math.NT2017★ 1 cited

A shifted convolution sum for $G L (3) \times G L (2)$

Ping Xi

In this paper, we estimate the shifted convolution sum \[\sum_{n\geqslant1}λ_1(1,n)λ_2(n+h)V\Big(\frac{n}{X}\Big),\] where $V$ is a smooth function with support in $[1, 2]$ , $1\leqs…

math.NT2016★ 6 cited

Quadratic polynomials at prime arguments

Jie Wu, Ping Xi

For a fixed quadratic irreducible polynomial $f$ with no fixed prime factors at prime arguments, we prove that there exist infinitely many primes $p$ such that $f (p)$ has at most 4…

math.NT2016★ 3 cited

Arithmetic exponent pairs for algebraic trace functions and applications

Jie Wu, Ping Xi

We study short sums of algebraic trace functions via the $q$ -analogue of van der Corput method, and develop methods of arithmetic exponent pairs that coincide with the classical ca…

math.NT2013

Sign changes of Kloosterman sums with almost prime moduli

Ping Xi

We prove that the Kloosterman sum $S (1, 1; c)$ can change sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results…

math.NT2012

Sumsets in primes containing almost all even positive integers

Ping Xi

Let $A$ be a subset of primes up to $x$ . If we assume $A$ is well-distributed (in the Siegel-Walfisz sense) in any arithmetic progressions to moduli $q ⩽ (lo g x)^{c}$ for any…

math.NT2011★ 1 cited

Incomplete Kloosterman sums and Hooley's R $^{*}$ -Conjecture

Ping Xi

This paper has been withdrawn by the author because Proposition 1 is not valid.

math.NT2011

Asymptotic behaviors of Kloosterman sums

Ping Xi

This paper has been withdrawn by the author because there is a gap in Lemma 9.

math.NT2011

Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes

Ping Xi

In this paper, we prove a quantitative version of the statement that every nonempty finite subset of $N^{+}$ is a set of quadratic residues for infinitely many primes of the…

math.NT2011

A note on the moments of Kloosterman sums

Ping Xi, Yuan Yi

In this note, we deduce an asymptotic formula for even power moments of Kloosterman sums based on the important work of N. M. Katz on Kloosterman sheaves. In a similar manner, we c…

math.NT2010

Mean values of character sums analogue of Kloosterman sums

Ping Xi

Let $q$ be a positive integer, $χ$ a nontrivial character mod $q$ , $I$ an interval of length not exceeding $q .$ In this paper we shall study the character sum analogue of…

math.NT2009

On character sums over flat numbers

Ping Xi, Yuan Yi

Let $q ⩾ 2$ be an integer, $χ$ be any non-principal character mod $q$ , and $H = H (q) ⩽ q .$ In this paper the authors prove some estimates for character sums of the form…

Horizontal moments of Kloosterman sums and a density version of sieves

A uniform Weyl bound for L-functions of Hilbert modular forms

A double character sum of Conrey-Iwaniec and Petrow-Young

Bilinear forms with trace functions over arbitrary sets, and applications to Sato-Tate

Bounds on bilinear forms with Kloosterman sums

A conjecture of Sárközy on quadratic residues, II

Lang--Trotter Conjecture for CM Elliptic Curves

Moments and equidistributions of multiplicative analogues of Kloosterman sums

Addendum to "Arithmetic exponent pairs of algebraic trace functions and applications"

Equidistributions of Jacobi sums

When Kloosterman sums meet Hecke eigenvalues

Counting fundamental solutions to the Pell equation with prescribed size

A shifted convolution sum for GL(3)×GL(2)

Quadratic polynomials at prime arguments

Arithmetic exponent pairs for algebraic trace functions and applications

Sign changes of Kloosterman sums with almost prime moduli

Sumsets in primes containing almost all even positive integers

Incomplete Kloosterman sums and Hooley's R∗-Conjecture

Asymptotic behaviors of Kloosterman sums

Quadratic residues and non-residues for infinitely many Piatetski-Shapiro primes

A note on the moments of Kloosterman sums

Mean values of character sums analogue of Kloosterman sums

On character sums over flat numbers

A shifted convolution sum for $G L (3) \times G L (2)$

Incomplete Kloosterman sums and Hooley's R $^{*}$ -Conjecture