Sieving rational points on varieties
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- by Tim Browning and Daniel Loughran PDF
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Abstract:
An upper bound sieve for rational points on suitable varieties is developed, together with applications to counting rational points in thin sets, to local solubility in families, and to the notion of “friable” rational points with respect to divisors. In the special case of quadrics, sharper estimates are obtained by developing a version of the Selberg sieve for rational points.References
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Additional Information
- Tim Browning
- Affiliation: School of Mathematics, University of Bristol, Bristol BS8 1TW, United Kingdom
- Address at time of publication: IST Austria, 3400 Klosterneuburg, Austria
- MR Author ID: 703078
- Email: t.d.browning@bristol.ac.uk, tdb@ist.ac.at
- Daniel Loughran
- Affiliation: School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
- MR Author ID: 922680
- Email: daniel.loughran@manchester.ac.uk
- Received by editor(s): November 6, 2017
- Received by editor(s) in revised form: January 17, 2018
- Published electronically: September 18, 2018
- Additional Notes: During the preparation of this paper the first author was supported by EPSRC Grant No. EP/P026710/1 and by the NSF under Grant No. DMS-1440140, while in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the spring 2017 semester.
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 5757-5785
- MSC (2010): Primary 14G05, 11N36, 11P55, 14D10
- DOI: https://doi.org/10.1090/tran/7514
- MathSciNet review: 3937309