MINOR ARC MOMENTS OF WEYL SUMS

MINOR ARC MOMENTS OF WEYL SUMS

We obtain an improved bound for the 2k-th moment of a degree k Weyl sum, restricted to a set of minor arcs, when k is small. We then present some applications of this bound to some Diophantine problems, including a case of the Waring–Goldbach problem, and a particular family of Diophantine equations...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Glasgow mathematical journal 2013-01, Vol.55 (1), p.97-113
1. Verfasser: HARVEY, M. P.
Format: Artikel
Sprache:eng
Schlagworte:
Diophantine equation
Mathematical analysis
Norms
Number theory
Sums
Theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We obtain an improved bound for the 2k-th moment of a degree k Weyl sum, restricted to a set of minor arcs, when k is small. We then present some applications of this bound to some Diophantine problems, including a case of the Waring–Goldbach problem, and a particular family of Diophantine equations defined as the sum of a norm form and a diagonal form.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089512000365