The Waring Problem with the Ramanujan $au$-Function, II

[摘要] Let $au(n)$ be the Ramanujan $au$-function. We prove that forany integer $N$ with $|N|ge 2$ the diophantine equation$$sum_{i=1}^{148000}au(n_i)=N$$ has a solution in positiveintegers $n_1, n_2,ldots, n_{148000}$ satisfying the condition$$max_{1le ile 148000}n_ill |N|^{2/11}e^{-clog |N|/loglog|N|},$$ for some absolute constant $c>0.$

[学科分类] 数学（综合）

[关键词] Riemann zeta function;xi function;zeta zeros