24 citations · 171 across the 47 of their papers we have counts for
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math.NT2012
Rational points on pencils of conics and quadrics with many degenerate fibres
Tim Browning, Lilian Matthiesen, Alexei Skorobogatov
For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction control…
math.NT2012★ 14 cited
Cubic hypersurfaces and a version of the circle method for number fields
Tim Browning, Pankaj Vishe
A version of the Hardy-Littlewood circle method is developed for number fields K/Q and is used to show that non-singular projective cubic hypersurfaces over K always have a K-ratio…
math.NT2012★ 1 cited
Incomplete Kloosterman sums and multiplicative inverses in short intervals
Tim Browning, Alan Haynes
We investigate the solubility of the congruence xy=1 (mod p), where p is a prime and x,y are restricted to lie in suitable short intervals. Our work relies on a mean value theorem…