On the exponential sum over k-free numbers

J Brudern; A Granville; A Perelli; RC Vaughan; TD Wooley

On the exponential sum over k-free numbers

J Brudern^*, A Granville, A Perelli, RC Vaughan, TD Wooley

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

20 Citations (Scopus)

Abstract

This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We also provide non-trivial estimates for the L-2-means of such generating functions restricted to the minor arcs occurring in Hardy-Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach.

Original language	English
Pages (from-to)	739-761
Number of pages	23
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	356
Issue number	1738
Publication status	Published - 15 Mar 1998

Keywords

L-1-means
k-free numbers
exponential sums
Hardy-Littlewood method
binary additive representations
square-free numbers
WARINGS PROBLEM

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title = "On the exponential sum over k-free numbers",

abstract = "This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We also provide non-trivial estimates for the L-2-means of such generating functions restricted to the minor arcs occurring in Hardy-Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach.",

keywords = "L-1-means, k-free numbers, exponential sums, Hardy-Littlewood method, binary additive representations, square-free numbers, WARINGS PROBLEM",

author = "J Brudern and A Granville and A Perelli and RC Vaughan and TD Wooley",

year = "1998",

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journal = "Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences",

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TY - JOUR

T1 - On the exponential sum over k-free numbers

AU - Brudern, J

AU - Granville, A

AU - Perelli, A

AU - Vaughan, RC

AU - Wooley, TD

PY - 1998/3/15

Y1 - 1998/3/15

N2 - This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We also provide non-trivial estimates for the L-2-means of such generating functions restricted to the minor arcs occurring in Hardy-Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach.

AB - This paper is concerned with mean values of exponential sum generating functions over k-free numbers, and especially their L-1-means. We also provide non-trivial estimates for the L-2-means of such generating functions restricted to the minor arcs occurring in Hardy-Littlewood dissections, thereby permitting the circle method to be successfully applied to certain additive problems hitherto beyond its reach.

KW - L-1-means

KW - k-free numbers

KW - exponential sums

KW - Hardy-Littlewood method

KW - binary additive representations

KW - square-free numbers

KW - WARINGS PROBLEM

M3 - Article (Academic Journal)

SN - 1364-503X

VL - 356

SP - 739

EP - 761

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 1738

ER -

On the exponential sum over k-free numbers

Abstract

Keywords

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