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math.NT2009
Least zero of a cubic form
T. D. Browning, R. Dietmann, P. D. T. A. Elliott
An effective search bound is established for the least non-trivial integer zero of an arbitrary integral cubic form in at least 17 variables.
math.NT2009
Linear growth for Châtelet surfaces
T. D. Browning
An upper bound of the expected order of magnitude is established for the number of rational points of bounded height on Châtelet surfaces defined over the rationals.