4 papers
Selberg sieve weights and sign changes of Kloosterman sums. II. Square-free moduli with at most four prime factors
Yixiu Xiao, Hongze Li
Let \(\Kl(1;q)\) denote the normalized Kloosterman sum modulo \(q\). We prove that, for each sign, there are \(\gg X/\log X\) square-free moduli \(q\in(X,2X]\) with at most four pr…
Selberg sieve weights and sign changes of Kloosterman sums. I. Uniform asymptotics for shifted weights
Yixiu Xiao, Hongze Li
We prove an asymptotic formula for correlations of divisor sums with quadratic cutoff functions shifted independently by \(s,u\in[0,1/2]\). The error is \(O_g(Y/(\log Y)^2)\), unif…
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 =…
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