Some remarks on Gauss sums associated with kth powers

HL MONTGOMERY; RC VAUGHAN; TD WOOLEY; Trevor D Wooley

doi:10.1017/S0305004100073424

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 journal › Article (Academic Journal) › peer-review

24 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 language	English
Pages (from-to)	21-33
Number of pages	13
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	118
Issue number	1
DOIs	https://doi.org/10.1017/S0305004100073424
Publication status	Published - Jul 1995

Keywords

LARGE PRIME MODULUS
ADDITIVE CONGRUENCES

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title = "Some remarks on Gauss sums associated with kth powers",

abstract = "Estimates for rational trigonometric sums are of great importance in analysing the local aspects of many additive problems. Indeed, bounds for the sumsin which e(α) denotes exp (2πiα), play a fundamental r{\^o}le 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 ",

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author = "HL MONTGOMERY and RC VAUGHAN and TD WOOLEY and Wooley, {Trevor D}",

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language = "English",

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T1 - Some remarks on Gauss sums associated with kth powers

AU - MONTGOMERY, HL

AU - VAUGHAN, RC

AU - WOOLEY, TD

AU - Wooley, Trevor D

PY - 1995/7

Y1 - 1995/7

N2 - Estimates for rational trigonometric sums are of great importance in analysing the local aspects of many additive problems. Indeed, bounds for the sumsin 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

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

KW - LARGE PRIME MODULUS

KW - ADDITIVE CONGRUENCES

U2 - 10.1017/S0305004100073424

DO - 10.1017/S0305004100073424

M3 - Article (Academic Journal)

VL - 118

SP - 21

EP - 33

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -

Some remarks on Gauss sums associated with kth powers

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