most citedAn improvement on Gauss's Circle Problem and Dirichlet's Divisor Problem

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math.CA2023

A Stein-Tomas type estimate and a decoupling inequality

Xiaochun Li

A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.

math.CA2023

A remark on the mean value inequalities related to Waring's problem

Xiaochun Li

Assuming some pointwise estimates on certain Weyl's sum, we prove the sharp estimates of the mean value associated to the following exponential sum $$ \sum_{n=1}^N e^{2πi tn^d +2πi…