Cubic moments of Fourier coefficients and pairs of diagonal quartic forms

Abstract

We establish the non-singular Hasse Principle for pairs of diagonal quartic equations in 22 or more variables. Our methods involve the estimation of a certain entangled two-dimensional 21st moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.

References in corpus (1)

• The Hasse principle for systems of diagonal cubic forms