Quasi-diagonal behaviour and smooth Weyl sums

TD Wooley

Quasi-diagonal behaviour and smooth Weyl sums

TD Wooley^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Estimates are provided for small moments of exponential sums over smooth numbers substantially sharper than available hitherto. These bounds arise from the author's recent breaking of "classical convexity" in Waring's problem. The methods underlying these new estimates provide guidance on good choices of parameters in the new iterative methods for smaller exponents. 1991 Mathematics Subject Classification: 11L15, 11L07, 11P55.

Original language	English
Pages (from-to)	161-170
Number of pages	10
Journal	Monatshefte für Mathematik
Volume	130
Issue number	2
Publication status	Published - 2000

Keywords

exponential sums
mean value estimates
smooth Weyl sums
ITERATIVE METHOD
WARINGS PROBLEM
POWERS
CUBES

Cite this

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title = "Quasi-diagonal behaviour and smooth Weyl sums",

abstract = "Estimates are provided for small moments of exponential sums over smooth numbers substantially sharper than available hitherto. These bounds arise from the author's recent breaking of {"}classical convexity{"} in Waring's problem. The methods underlying these new estimates provide guidance on good choices of parameters in the new iterative methods for smaller exponents. 1991 Mathematics Subject Classification: 11L15, 11L07, 11P55.",

keywords = "exponential sums, mean value estimates, smooth Weyl sums, ITERATIVE METHOD, WARINGS PROBLEM, POWERS, CUBES",

author = "TD Wooley",

year = "2000",

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pages = "161--170",

journal = "Monatshefte f{\"u}r Mathematik",

issn = "0026-9255",

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TY - JOUR

T1 - Quasi-diagonal behaviour and smooth Weyl sums

AU - Wooley, TD

PY - 2000

Y1 - 2000

N2 - Estimates are provided for small moments of exponential sums over smooth numbers substantially sharper than available hitherto. These bounds arise from the author's recent breaking of "classical convexity" in Waring's problem. The methods underlying these new estimates provide guidance on good choices of parameters in the new iterative methods for smaller exponents. 1991 Mathematics Subject Classification: 11L15, 11L07, 11P55.

AB - Estimates are provided for small moments of exponential sums over smooth numbers substantially sharper than available hitherto. These bounds arise from the author's recent breaking of "classical convexity" in Waring's problem. The methods underlying these new estimates provide guidance on good choices of parameters in the new iterative methods for smaller exponents. 1991 Mathematics Subject Classification: 11L15, 11L07, 11P55.

KW - exponential sums

KW - mean value estimates

KW - smooth Weyl sums

KW - ITERATIVE METHOD

KW - WARINGS PROBLEM

KW - POWERS

KW - CUBES

M3 - Article (Academic Journal)

VL - 130

SP - 161

EP - 170

JO - Monatshefte für Mathematik

JF - Monatshefte für Mathematik

SN - 0026-9255

IS - 2

ER -