The Hasse principle for systems of quadratic and cubic diagonal equations

2016/12/02 by Brandes, Julia
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1612.00719

Abstract

Employing Brüdern's and Wooley's new complification method, we establish an asymptotic Hasse principle for the number of solutions to a system of r₃ cubic and r₂ quadratic diagonal forms, when the number of cubic equations is at least double the number of quadratic forms. The number of variables required is lower than in earlier work. In particular, we achieve essentially square root cancellation for systems of one quadratic and arbitrarily many cubic equations.

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