From the 1 of 6 linked papers with an AI index.
6 papers
Large sieve inequality for sums of Legendre symbols over short intervals
Marc Munsch, Igor Shparlinski, Yu-Chen Sun +1
The paper establishes a nontrivial upper bound for the second moment of sums of Legendre symbols over short intervals using the Burgess bound and Selberg sieve, showing that for mo…
Kloosterman sign changes with moduli having at most five prime factors
Yixiu Xiao
On square-free moduli having at most five prime factors, we prove that each sign of the normalized Kloosterman sum occurs times…
Moment Estimates and Discrepancy for Sums of Square Roots Modulo One
Yixiu Xiao
Let be fixed. We study the distribution modulo one of the sums \begin{equation*} \sqrt{a_1} + \cdots + \sqrt{a_k}, \qquad 1\le a_1, \dots, a_k \le n, \end{equation*}…
Least zero of pairs of additive cubic equations
Yixiu Xiao, Hongze Li
An effective upper bound is established for the least non-trivial integer solution to the system of cubic forms \[ \begin{cases} F = c_{1}x_1^3 + c_{2}x_2^3 + \cdots + c_{n}x_n^3 =…
Shifted bilinear sums of Salié sums and the distribution of modular square roots of shifted primes
Igor E. Shparlinski, Yixiu Xiao
We establish various upper bounds on Type-I and Type-II shifted bilinear sums with Salié sums modulo a large prime . We use these bounds to study, for fixed integers $a,b\not \…
Least zero of a cubic form
Yixiu Xiao, Hongze Li
An explicit upper bound is established for the least non-trivial integer zero of an arbitrary cubic form provided that