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RATIONAL POINTS ON INTERSECTIONS OF CUBIC AND QUADRIC HYPERSURFACES

Part of: Additive number theory; partitions Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  05 June 2014

T. D. Browning ,
R. Dietmann  and
D. R. Heath-Brown
T. D. Browning
Affiliation:
School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK (t.d.browning@bristol.ac.uk)
R. Dietmann
Affiliation:
Department of Mathematics, Royal Holloway, University of London, Egham, TW20 OEX, UK (rainer.dietmann@rhul.ac.uk)
D. R. Heath-Brown
Affiliation:
Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK (rhb@maths.ox.ac.uk)
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Abstract

We investigate the Hasse principle for complete intersections cut out by a quadric hypersurface and a cubic hypersurface defined over the rational numbers.

Keywords

Hasse principlecubicquadraticsystemrational pointDiophantine equationscircle methodWeyl sumvan der Corput methodcomplete intersection

MSC classification

Primary: 11G35: Varieties over global fields 11P55: Applications of the Hardy-Littlewood method 14G05: Rational points
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 14 , Issue 4 , October 2015 , pp. 703 - 749
Copyright
© Cambridge University Press 2014 

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