Geodesic
Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi
Acta Arithmetica, Tome 85 (1998) no. 1, pp. 13-33.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of Hooley on the average of the square of the number of representations.
DOI : 10.4064/aa-85-1-13-33

Jean-Marc Deshouillers 1 ; François Hennecart 1 ; Bernard Landreau 1

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Jean-Marc Deshouillers; François Hennecart; Bernard Landreau. Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi. Acta Arithmetica, Tome 85 (1998) no. 1, pp. 13-33. doi : 10.4064/aa-85-1-13-33. http://geodesic.mathdoc.fr/articles/10.4064/aa-85-1-13-33/

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