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

Canadian mathematical bulletin

关键词: Riemann zeta function;    xi function;    zeta zeros;   

DOI  :  10.4153/CMB-2009-022-2

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 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 $c>0.$

【 授权许可】

Unknown