{"abstract":[{"lang":"eng","text":"A version of the Hardy-Littlewood circle method is developed for number fields K/ℚ and is used to show that nonsingular projective cubic hypersurfaces over K always have a K-rational point when they have dimension at least 8. "}],"_id":"249","date_created":"2018-12-11T11:45:26Z","page":"1825 - 1883","intvolume":"       163","month":"07","publisher":"Duke University Press","quality_controlled":0,"author":[{"last_name":"Browning","orcid":"0000-0002-8314-0177","full_name":"Timothy Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","first_name":"Timothy D"},{"last_name":"Vishe","full_name":"Vishe, Pankaj","first_name":"Pankaj"}],"day":"01","title":"Cubic hypersurfaces and a version of the circle method for number fields","doi":"10.1215/00127094-2738530","publication_status":"published","date_updated":"2021-01-12T06:57:47Z","issue":"10","status":"public","year":"2014","extern":1,"type":"journal_article","publication":"Duke Mathematical Journal","publist_id":"7653","volume":163,"citation":{"apa":"Browning, T. D., &#38; Vishe, P. (2014). Cubic hypersurfaces and a version of the circle method for number fields. <i>Duke Mathematical Journal</i>. Duke University Press. <a href=\"https://doi.org/10.1215/00127094-2738530\">https://doi.org/10.1215/00127094-2738530</a>","chicago":"Browning, Timothy D, and Pankaj Vishe. “Cubic Hypersurfaces and a Version of the Circle Method for Number Fields.” <i>Duke Mathematical Journal</i>. Duke University Press, 2014. <a href=\"https://doi.org/10.1215/00127094-2738530\">https://doi.org/10.1215/00127094-2738530</a>.","mla":"Browning, Timothy D., and Pankaj Vishe. “Cubic Hypersurfaces and a Version of the Circle Method for Number Fields.” <i>Duke Mathematical Journal</i>, vol. 163, no. 10, Duke University Press, 2014, pp. 1825–83, doi:<a href=\"https://doi.org/10.1215/00127094-2738530\">10.1215/00127094-2738530</a>.","short":"T.D. Browning, P. Vishe, Duke Mathematical Journal 163 (2014) 1825–1883.","ieee":"T. D. Browning and P. Vishe, “Cubic hypersurfaces and a version of the circle method for number fields,” <i>Duke Mathematical Journal</i>, vol. 163, no. 10. Duke University Press, pp. 1825–1883, 2014.","ista":"Browning TD, Vishe P. 2014. Cubic hypersurfaces and a version of the circle method for number fields. Duke Mathematical Journal. 163(10), 1825–1883.","ama":"Browning TD, Vishe P. Cubic hypersurfaces and a version of the circle method for number fields. <i>Duke Mathematical Journal</i>. 2014;163(10):1825-1883. doi:<a href=\"https://doi.org/10.1215/00127094-2738530\">10.1215/00127094-2738530</a>"},"date_published":"2014-07-01T00:00:00Z"}