Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi

• Autorzy: Jean-Marc Deshouillers , François Hennecart , Bernard Landreau
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60F99: None of the above, but in this section
• 11P05: Waring's problem and variants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 1
• Strony: 13-33

Daty

wydano

1998

otrzymano

1996-11-15

poprawiono

1997-10-10

Twórcy

autor

Jean-Marc Deshouillers

• Mathématiques Stochastiques, Université Victor Segalen Bordeaux 2, F-33076 Bordeaux Cedex, France

autor

François Hennecart

• Laboratoire d'Algorithmique Arithmétique Expérimentale, Unité Mixte de Recherche CNRS 9936, Université Bordeaux I, F-33405 Talence Cedex, France

autor

Bernard Landreau

• Laboratoire d'Algorithmique Arithmétique Expérimentale, Unité Mixte de Recherche CNRS 9936, Université Bordeaux I, F-33405 Talence Cedex, France

Bibliografia

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