Diophantine inequalities and quasi-algebraically closed fields

Craig V. Spencer; Trevor D. Wooley

doi:10.1007/s11856-012-0004-5

Diophantine inequalities and quasi-algebraically closed fields

Craig V. Spencer^*, Trevor D. Wooley

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.

Original language	English
Pages (from-to)	721-738
Number of pages	18
Journal	Israel Journal of Mathematics
Volume	191
Issue number	2
DOIs	https://doi.org/10.1007/s11856-012-0004-5
Publication status	Published - Oct 2012

Keywords

CUBIC EQUATIONS
THEOREM

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10.1007/s11856-012-0004-5

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title = "Diophantine inequalities and quasi-algebraically closed fields",

abstract = "Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.",

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T1 - Diophantine inequalities and quasi-algebraically closed fields

AU - Spencer, Craig V.

AU - Wooley, Trevor D.

PY - 2012/10

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N2 - Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.

AB - Consider a form g(x (1),...,x (s) ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d (2), then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.

KW - CUBIC EQUATIONS

KW - THEOREM

U2 - 10.1007/s11856-012-0004-5

DO - 10.1007/s11856-012-0004-5

M3 - Article (Academic Journal)

VL - 191

SP - 721

EP - 738

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 2

ER -

Diophantine inequalities and quasi-algebraically closed fields

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Keywords

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