[{"issue":"2","day":"01","publisher":"John Wiley and Sons Ltd","extern":1,"type":"journal_article","doi":"10.1112/plms/pdm032","month":"03","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."}],"volume":96,"date_updated":"2021-01-12T06:56:13Z","publication_status":"published","quality_controlled":0,"title":"On the representation of integers by quadratic forms","_id":"224","publication":"Proceedings of the London Mathematical Society","intvolume":" 96","date_created":"2018-12-11T11:45:18Z","page":"389 - 416","publist_id":"7688","author":[{"last_name":"Browning","full_name":"Timothy Browning","first_name":"Timothy D","orcid":"0000-0002-8314-0177","id":"35827D50-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Dietmann, Rainer","last_name":"Dietmann","first_name":"Rainer"}],"year":"2008","date_published":"2008-03-01T00:00:00Z","citation":{"ista":"Browning TD, Dietmann R. 2008. On the representation of integers by quadratic forms. Proceedings of the London Mathematical Society. 96(2), 389–416.","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","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","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.","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.","short":"T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society 96 (2008) 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."},"status":"public"}]