---
_id: '224'
abstract:
- lang: eng
text: Let n ≥ 4 and let Q ∈ [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:
- first_name: Timothy D
full_name: Timothy Browning
id: 35827D50-F248-11E8-B48F-1D18A9856A87
last_name: Browning
orcid: 0000-0002-8314-0177
- first_name: Rainer
full_name: Dietmann, Rainer
last_name: Dietmann
citation:
ama: Browning TD, Dietmann R. On the representation of integers by quadratic forms.
*Proceedings of the London Mathematical Society*. 2008;96(2):389-416. doi:10.1112/plms/pdm032
apa: Browning, T. D., & Dietmann, R. (2008). On the representation of integers
by quadratic forms. *Proceedings of the London Mathematical Society*. John
Wiley and Sons Ltd. https://doi.org/10.1112/plms/pdm032
chicago: Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers
by Quadratic Forms.” *Proceedings of the London Mathematical Society*. John
Wiley and Sons Ltd, 2008. https://doi.org/10.1112/plms/pdm032.
ieee: T. D. Browning and R. Dietmann, “On the representation of integers by quadratic
forms,” *Proceedings of the London Mathematical Society*, vol. 96, no. 2.
John Wiley and Sons Ltd, pp. 389–416, 2008.
ista: Browning TD, Dietmann R. 2008. On the representation of integers by quadratic
forms. Proceedings of the London Mathematical Society. 96(2), 389–416.
mla: Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers
by Quadratic Forms.” *Proceedings of the London Mathematical Society*, vol.
96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:10.1112/plms/pdm032.
short: T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society
96 (2008) 389–416.
date_created: 2018-12-11T11:45:18Z
date_published: 2008-03-01T00:00:00Z
date_updated: 2021-01-12T06:56:13Z
day: '01'
doi: 10.1112/plms/pdm032
extern: 1
intvolume: ' 96'
issue: '2'
month: '03'
page: 389 - 416
publication: Proceedings of the London Mathematical Society
publication_status: published
publisher: John Wiley and Sons Ltd
publist_id: '7688'
quality_controlled: 0
status: public
title: On the representation of integers by quadratic forms
type: journal_article
volume: 96
year: '2008'
...