3 papers
math.NT2026
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*}…
math.NT2026
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 \e…
math.NT2025
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 =…