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A PAUCITY ESTIMATE RELATED TO NEWTON SUMS OF ODD DEGREE

Published online by Cambridge University Press:  27 March 2012

Jörg Brüdern
Affiliation:
Mathematisches Institut, Bunsenstrasse 3–5, D 37073 Göttingen, Germany (email: bruedern@uni-math.gwdg.de)
Olivier Robert
Affiliation:
Institut Camille Jordan CNRS UMR 5208, Université de Lyon and Université de Saint-Etienne, 23, rue du Dr P. Michelon, F-42000, Saint-Etienne, France (email: olivier.robert@univ-st-etienne.fr)
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Abstract

Paucity is established for a system of diagonal diophantine equations, in which the degrees are the odd numbers in ascending order.

Type
Research Article
Copyright
Copyright © University College London 2012

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References

[1]de la Bretèche, R., Répartition des points rationnels sur la cubique de Segre. Proc. Lond. Math. Soc. (3) 95 (2007), 69155.CrossRefGoogle Scholar
[2]Borchardt, C. W., Über eine Eigenschaft der Potenzsummen ungerader Ordnung. In Monatsberichte der Berliner Akademie, (1857), 24–34.Google Scholar
[3]Choudhry, A., The Diophantine system ∑ 41x ri=∑ 41y ri,r=1,3,5. Bull. Calcutta Math. Soc. 83 (1991), 8586.Google Scholar
[4]Foulkes, H. O., Theorems of Kakeya and Pólya on power-sums. Math. Z. 65 (1956), 345352.CrossRefGoogle Scholar
[5]Perron, O., Über die Abhängigkeit von Potenzsummen und einen Satz von Pólya. Math. Z. 63 (1955), 1930.CrossRefGoogle Scholar
[6]Perron, O., Über Potenzsummen. Math. Z. 64 (1956), 103114.CrossRefGoogle Scholar
[7]Robert, O., An analogue of van der Corput’s A 5-process for exponential sums. Mathematika 49 (2002), 167183.CrossRefGoogle Scholar
[8]Vaughan, R. C. and Wooley, T. D., A certain nonary cubic form and related equations. Duke Math. J. 80(3) (1995), 669735.CrossRefGoogle Scholar
[9]Vaughan, R. C. and Wooley, T. D., A special case of Vinogradov’s mean value theorem. Acta Arith. 79 (1997), 193204.CrossRefGoogle Scholar