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1. CMB 2009 (vol 52 pp. 195)
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The Waring Problem with the Ramanujan $\tau$-Function, II Let $\tau(n)$ be the Ramanujan $\tau$-function. We prove that for
any integer $N$ with $|N|\ge 2$ the diophantine equation
$$\sum_{i=1}^{148000}\tau(n_i)=N$$ has a solution in positive
integers $n_1, n_2,\ldots, n_{148000}$ satisfying the condition
$$\max_{1\le i\le 148000}n_i\ll |N|^{2/11}e^{-c\log |N|/\log\log
|N|},$$ for some absolute constant $c>0.$
Categories:11B13, 11F30 |