Some quantitative results related to Roth's theorem

E. Bombieri; A. J. Van Der Poorten

doi:10.1017/S1446788700030159

Some quantitative results related to Roth's theorem

E. Bombieri, A. J. Van Der Poorten

Macquarie University Administration Unit

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.

Original language	English
Pages (from-to)	233-248
Number of pages	16
Journal	Journal of the Australian Mathematical Society
Volume	45
Issue number	2
DOIs	https://doi.org/10.1017/S1446788700030159
Publication status	Published - 1988

Bibliographical note

Corrigendum can be found in Journal of the Australian Mathematical Society, 48(1), pp. 154-155, 1990.
https://doi.org/10.1017/S1446788700035291

Access to Document

10.1017/S1446788700030159

Cite this

@article{2f3c1072456b4b4eb43dd8292f8a8e7c,

title = "Some quantitative results related to Roth's theorem",

abstract = "We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.",

author = "E. Bombieri and {Van Der Poorten}, {A. J.}",

note = "Corrigendum can be found in Journal of the Australian Mathematical Society, 48(1), pp. 154-155, 1990. https://doi.org/10.1017/S1446788700035291",

year = "1988",

doi = "10.1017/S1446788700030159",

language = "English",

volume = "45",

pages = "233--248",

journal = "Journal of the Australian Mathematical Society",

issn = "1446-7887",

publisher = "Australian Mathematical Society",

number = "2",

}

TY - JOUR

T1 - Some quantitative results related to Roth's theorem

AU - Bombieri, E.

AU - Van Der Poorten, A. J.

N1 - Corrigendum can be found in Journal of the Australian Mathematical Society, 48(1), pp. 154-155, 1990. https://doi.org/10.1017/S1446788700035291

PY - 1988

Y1 - 1988

N2 - We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.

AB - We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.

UR - http://www.scopus.com/inward/record.url?scp=84974201270&partnerID=8YFLogxK

UR - https://doi.org/10.1017/S1446788700035291

U2 - 10.1017/S1446788700030159

DO - 10.1017/S1446788700030159

M3 - Article

AN - SCOPUS:84974201270

VL - 45

SP - 233

EP - 248

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 2

ER -

Some quantitative results related to Roth's theorem

Abstract

Bibliographical note

Access to Document

Fingerprint

Cite this