Some remarks on Gauss sums associated with kth powers

HL MONTGOMERY*, RC VAUGHAN, TD WOOLEY, Trevor D Wooley

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

23 Citations (Scopus)

Abstract

Estimates for rational trigonometric sums are of great importance in analysing the local aspects of many additive problems. Indeed, bounds for the sums

in which e(α) denotes exp (2πiα), play a fundamental rôle in the application of the Hardy–Littlewood method to Waring's problem (see [11]), and also in the analysis of the local solubility of systems of additive equations (see, for example, [2]). When k ≥ 2 is an integer, and p is a prime number it is well known (see [5] or [11, lemma 4·3]) that

Original languageEnglish
Pages (from-to)21-33
Number of pages13
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume118
Issue number1
DOIs
Publication statusPublished - Jul 1995

Keywords

  • LARGE PRIME MODULUS
  • ADDITIVE CONGRUENCES

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