Exceptional Sets for Diophantine Inequalities

Scott T. Parsell; Trevor D. Wooley

doi:10.1093/imrn/rnt062

Exceptional Sets for Diophantine Inequalities

Scott T. Parsell^*, Trevor D. Wooley

^*Corresponding author for this work

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

4 Citations (Scopus)

Abstract

We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N1-delta), for a positive number delta.

Original language	English
Pages (from-to)	3919-3974
Number of pages	56
Journal	International Mathematics Research Notices
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnt062
Publication status	Published - 2014

Keywords

MEAN-VALUE THEOREM
LATTICE POINT PROBLEMS
SMOOTH WEYL SUMS
WARINGS PROBLEM
ADDITIVE REPRESENTATION
ASYMPTOTIC FORMULAS
SMALLER EXPONENTS
QUADRATIC-FORMS
THIN SEQUENCES
HIGHER POWERS

Access to Document

10.1093/imrn/rnt062

Handle.net

Persistent link

Cite this

@article{0b52e382fa54469b932502e3326b98c9,

title = "Exceptional Sets for Diophantine Inequalities",

abstract = "We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N1-delta), for a positive number delta.",

keywords = "MEAN-VALUE THEOREM, LATTICE POINT PROBLEMS, SMOOTH WEYL SUMS, WARINGS PROBLEM, ADDITIVE REPRESENTATION, ASYMPTOTIC FORMULAS, SMALLER EXPONENTS, QUADRATIC-FORMS, THIN SEQUENCES, HIGHER POWERS",

author = "Parsell, {Scott T.} and Wooley, {Trevor D.}",

year = "2014",

doi = "10.1093/imrn/rnt062",

language = "English",

pages = "3919--3974",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "14",

}

TY - JOUR

T1 - Exceptional Sets for Diophantine Inequalities

AU - Parsell, Scott T.

AU - Wooley, Trevor D.

PY - 2014

Y1 - 2014

N2 - We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N1-delta), for a positive number delta.

AB - We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N1-delta), for a positive number delta.

KW - MEAN-VALUE THEOREM

KW - LATTICE POINT PROBLEMS

KW - SMOOTH WEYL SUMS

KW - WARINGS PROBLEM

KW - ADDITIVE REPRESENTATION

KW - ASYMPTOTIC FORMULAS

KW - SMALLER EXPONENTS

KW - QUADRATIC-FORMS

KW - THIN SEQUENCES

KW - HIGHER POWERS

U2 - 10.1093/imrn/rnt062

DO - 10.1093/imrn/rnt062

M3 - Article (Academic Journal)

SP - 3919

EP - 3974

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 14

ER -

Exceptional Sets for Diophantine Inequalities

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this