{"extern":"1","external_id":{"arxiv":["0611086"]},"day":"31","author":[{"id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D","last_name":"Browning","full_name":"Browning, Timothy D"},{"last_name":"Heath Brown","full_name":"Heath Brown, Roger","first_name":"Roger"}],"article_processing_charge":"No","_id":"164","abstract":[{"lang":"eng","text":"Let g be a cubic polynomial with integer coefficients and n>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 <n-10. The proof is based on the Hardy-Littlewood circle method."}],"date_published":"2009-01-31T00:00:00Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"type":"book_chapter","oa_version":"Preprint","oa":1,"publisher":"Cambridge University Press","year":"2009","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/math/0611086"}],"date_updated":"2020-05-12T08:33:19Z","title":"Integral points on cubic hypersurfaces","date_created":"2018-12-11T11:44:58Z","publication_status":"published","month":"01","quality_controlled":"1","publication":"Analytic Number Theory: Essays in honour of Klaus Roth","citation":{"mla":"Browning, Timothy D., and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” *Analytic Number Theory: Essays in Honour of Klaus Roth*, Cambridge University Press, 2009, pp. 75–90.","ista":"Browning TD, Heath Brown R. 2009. Integral points on cubic hypersurfaces. Analytic Number Theory: Essays in honour of Klaus Roth. 75–90.","ieee":"T. D. Browning and R. Heath Brown, “Integral points on cubic hypersurfaces,” in *Analytic Number Theory: Essays in honour of Klaus Roth*, Cambridge University Press, 2009, pp. 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.","ama":"Browning TD, Heath Brown R. Integral points on cubic hypersurfaces. In: *Analytic Number Theory: Essays in Honour of Klaus Roth*. Cambridge University Press; 2009:75-90.","chicago":"Browning, Timothy D, and Roger Heath Brown. “Integral Points on Cubic Hypersurfaces.” In *Analytic Number Theory: Essays in Honour of Klaus Roth*, 75–90. Cambridge University Press, 2009.","apa":"Browning, T. D., & Heath Brown, R. (2009). Integral points on cubic hypersurfaces. In *Analytic Number Theory: Essays in honour of Klaus Roth* (pp. 75–90). Cambridge University Press."},"publist_id":"7757","page":"75 - 90"}