{"title":"Integral points on cubic hypersurfaces","quality_controlled":"1","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","last_name":"Browning","orcid":"0000-0002-8314-0177","first_name":"Timothy D","full_name":"Browning, Timothy D"},{"first_name":"Roger","full_name":"Heath Brown, Roger","last_name":"Heath Brown"}],"_id":"164","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/math/0611086"}],"abstract":[{"lang":"eng","text":"Let g be a cubic polynomial with integer coefficients and n&gt;9 variables, and assume that the congruence g=0 modulo p^k is soluble for all prime powers p^k. We show that the equation g=0 has infinitely many integer solutions when the cubic part of g defines a projective hypersurface with singular locus of dimension &lt;n-10. The proof is based on the Hardy-Littlewood circle method."}],"oa_version":"Preprint","publication_status":"published","publication":"Analytic Number Theory: Essays in honour of Klaus Roth","type":"book_chapter","extern":"1","date_updated":"2021-01-12T06:52:11Z","publist_id":"7757","language":[{"iso":"eng"}],"external_id":{"arxiv":["0611086"]},"day":"31","page":"75 - 90","year":"2009","status":"public","publisher":"Cambridge University Press","oa":1,"date_published":"2009-01-31T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","date_created":"2018-12-11T11:44:58Z","month":"01","citation":{"chicago":"Browning, Timothy D, and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” In <i>Analytic Number Theory: Essays in Honour of Klaus Roth</i>, 75–90. Cambridge University Press, 2009.","ista":"Browning TD, Heath Brown R. 2009.Integral points on cubic hypersurfaces. In: Analytic Number Theory: Essays in honour of Klaus Roth. , 75–90.","apa":"Browning, T. D., &#38; Heath Brown, R. (2009). Integral points on cubic hypersurfaces. In <i>Analytic Number Theory: Essays in honour of Klaus Roth</i> (pp. 75–90). Cambridge University Press.","mla":"Browning, Timothy D., and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” <i>Analytic Number Theory: Essays in Honour of Klaus Roth</i>, Cambridge University Press, 2009, pp. 75–90.","ama":"Browning TD, Heath Brown R. Integral points on cubic hypersurfaces. In: <i>Analytic Number Theory: Essays in Honour of Klaus Roth</i>. Cambridge University Press; 2009:75-90.","short":"T.D. Browning, R. Heath Brown, in:, Analytic Number Theory: Essays in Honour of Klaus Roth, Cambridge University Press, 2009, pp. 75–90.","ieee":"T. D. Browning and R. Heath Brown, “Integral points on cubic hypersurfaces,” in <i>Analytic Number Theory: Essays in honour of Klaus Roth</i>, Cambridge University Press, 2009, pp. 75–90."}}