{"title":"On the representation of integers by quadratic forms","doi":"10.1112/plms/pdm032","date_updated":"2021-01-12T06:56:13Z","date_created":"2018-12-11T11:45:18Z","page":"389 - 416","date_published":"2008-03-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"issue":"2","publisher":"John Wiley and Sons Ltd","publist_id":"7688","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Timothy Browning","last_name":"Browning"},{"full_name":"Dietmann, Rainer","first_name":"Rainer","last_name":"Dietmann"}],"month":"03","publication_status":"published","intvolume":"        96","quality_controlled":0,"day":"01","citation":{"mla":"Browning, Timothy D., and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2, John Wiley and Sons Ltd, 2008, pp. 389–416, doi:<a href=\"https://doi.org/10.1112/plms/pdm032\">10.1112/plms/pdm032</a>.","ama":"Browning TD, Dietmann R. On the representation of integers by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. 2008;96(2):389-416. doi:<a href=\"https://doi.org/10.1112/plms/pdm032\">10.1112/plms/pdm032</a>","short":"T.D. Browning, R. Dietmann, Proceedings of the London Mathematical Society 96 (2008) 389–416.","chicago":"Browning, Timothy D, and Rainer Dietmann. “On the Representation of Integers by Quadratic Forms.” <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd, 2008. <a href=\"https://doi.org/10.1112/plms/pdm032\">https://doi.org/10.1112/plms/pdm032</a>.","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., &#38; Dietmann, R. (2008). On the representation of integers by quadratic forms. <i>Proceedings of the London Mathematical Society</i>. John Wiley and Sons Ltd. <a href=\"https://doi.org/10.1112/plms/pdm032\">https://doi.org/10.1112/plms/pdm032</a>","ieee":"T. D. Browning and R. Dietmann, “On the representation of integers by quadratic forms,” <i>Proceedings of the London Mathematical Society</i>, vol. 96, no. 2. John Wiley and Sons Ltd, pp. 389–416, 2008."},"type":"journal_article","_id":"224","publication":"Proceedings of the London Mathematical Society","year":"2008","status":"public","extern":1,"volume":96}