On the representation of integers by quadratic forms

TD Browning; R Dietmann

doi:10.1112/plms/pdm032

On the representation of integers by quadratic forms

TD Browning, R Dietmann

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

14 Citations (Scopus)

Abstract

Let n ≥ 4 and let Q ∈ ℤ[X1, …, Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

Translated title of the contribution	On the representation of integers by quadratic forms
Original language	English
Pages (from-to)	289 - 416
Number of pages	28
Journal	Proceedings of the London Mathematical Society
Volume	96 (2)
DOIs	https://doi.org/10.1112/plms/pdm032
Publication status	Published - Mar 2008

Bibliographical note

Publisher: Oxford University Press
Other: arXiv:math/0603358

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10.1112/plms/pdm032

http://plms.oxfordjournals.org/cgi/content/abstract/96/2/389

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title = "On the representation of integers by quadratic forms",

abstract = "Let n ≥ 4 and let Q ∈ ℤ[X1, …, Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.",

author = "TD Browning and R Dietmann",

note = "Publisher: Oxford University Press Other: arXiv:math/0603358",

year = "2008",

month = mar,

doi = "10.1112/plms/pdm032",

language = "English",

volume = "96 (2)",

pages = "289 -- 416",

journal = "Proceedings of the London Mathematical Society",

issn = "1460-244X",

publisher = "Oxford University Press",

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T1 - On the representation of integers by quadratic forms

AU - Browning, TD

AU - Dietmann, R

N1 - Publisher: Oxford University Press Other: arXiv:math/0603358

PY - 2008/3

Y1 - 2008/3

N2 - Let n ≥ 4 and let Q ∈ ℤ[X1, …, Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

AB - Let n ≥ 4 and let Q ∈ ℤ[X1, …, Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

U2 - 10.1112/plms/pdm032

DO - 10.1112/plms/pdm032

M3 - Article (Academic Journal)

SN - 1460-244X

VL - 96 (2)

SP - 289

EP - 416

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

ER -

On the representation of integers by quadratic forms

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