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

7 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

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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.",

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AU - Parsell, Scott T.

AU - Wooley, Trevor D.

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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

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DO - 10.1093/imrn/rnt062

M3 - Article (Academic Journal)

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SP - 3919

EP - 3974

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 14

ER -

Exceptional Sets for Diophantine Inequalities

Abstract

Keywords

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