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Cubic moments of Fourier coefficients and pairs of diagonal quartic forms

Jörg Brüdern, Trevor D. Wooley (2015)

Journal of the European Mathematical Society

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.

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