Geodesic
The Waring Problem with the Ramanujan τ -Function, II
Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 195-199

Voir la notice de l'article provenant de la source Cambridge University Press

Let $\tau \left( n \right)$ be the Ramanujan $\text{ }\!\!\tau\!\!\text{ }$ -function. We prove that for any integer $N$ with $\left| N \right|\,\ge \,2$ the diophantine equation $$\underset{i=1}{\overset{148000}{\mathop{\sum }}}\,\,\tau \left( {{n}_{i}} \right)\,=\,N$$ has a solution in positive integers ${{n}_{1}},\,{{n}_{2}},\,.\,.\,.\,,\,{{n}_{148000}}$ satisfying the condition $$\underset{1\le i\le 148000}{\mathop{\max }}\,{{n}_{i}}\ll |N{{|}^{2/11}}{{e}^{-c\log |N|/\log \log |N|}},$$ for some absolute constant $c\,>\,0$ .
DOI : 10.4153/CMB-2009-022-2
Mots-clés : 11B13, 11F30 
Garaev, M. Z.; Garcia, V. C.; Konyagin, S. V. The Waring Problem with the Ramanujan τ -Function, II. Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 195-199. doi: 10.4153/CMB-2009-022-2
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