Mean value estimates for odd cubic Weyl sums

Trevor D. Wooley

doi:10.1112/blms/bdv066

Mean value estimates for odd cubic Weyl sums

Trevor D. Wooley

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

15 Citations (Scopus)

406 Downloads (Pure)

Abstract

We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.

Original language	English
Pages (from-to)	946-957
Number of pages	12
Journal	Bulletin of the London Mathematical Society
Volume	47
Issue number	6
Early online date	20 Oct 2015
DOIs	https://doi.org/10.1112/blms/bdv066
Publication status	Published - Dec 2015

Keywords

math.NT
11L15
11L07
11P55

Access to Document

10.1112/blms/bdv066

pdf
This is an accepted version of the article published in the Bulletin of the London Mathematical Society.
Accepted author manuscript, 182 KB

Handle.net

Persistent link

Cite this

@article{3c501f9d36a84cbab16eea20f6abbc47,

title = "Mean value estimates for odd cubic Weyl sums",

abstract = "We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument \$\textbackslash{}alpha x\textasciicircum{}3+\textbackslash{}beta x\$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.",

keywords = "math.NT, 11L15, 11L07, 11P55",

author = "Wooley, \{Trevor D.\}",

year = "2015",

month = dec,

doi = "10.1112/blms/bdv066",

language = "English",

volume = "47",

pages = "946--957",

journal = "Bulletin of the London Mathematical Society",

issn = "0024-6093",

publisher = "John Wiley \& Sons, Ltd.",

number = "6",

}

TY - JOUR

T1 - Mean value estimates for odd cubic Weyl sums

AU - Wooley, Trevor D.

PY - 2015/12

Y1 - 2015/12

N2 - We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.

AB - We establish an essentially optimal estimate for the ninth moment of the exponential sum having argument $\alpha x^3+\beta x$. The first substantial advance in this topic for over 60 years, this leads to improvements in Heath-Brown's variant of Weyl's inequality, and other applications of Diophantine type.

KW - math.NT

KW - 11L15

KW - 11L07

KW - 11P55

U2 - 10.1112/blms/bdv066

DO - 10.1112/blms/bdv066

M3 - Article (Academic Journal)

SN - 0024-6093

VL - 47

SP - 946

EP - 957

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 6

ER -

Mean value estimates for odd cubic Weyl sums

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this