The Hasse Principle for Pairs of Diagonal Cubic Forms
نویسندگان
چکیده
By means of the Hardy-Littlewood method, we apply a new mean value theorem for exponential sums to confirm the truth, over the rational numbers, of the Hasse principle for pairs of diagonal cubic forms in thirteen or more variables.
منابع مشابه
Cubic Moments of Fourier Coefficients and Pairs of Diagonal Quartic Forms
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 21 moment of quartic smooth Weyl sums via a novel cubic moment of Fourier coefficients.
متن کاملCubic Points on Cubic Curves and the Brauer-manin Obstruction on K3 Surfaces
We show that if over some number field there exists a certain diagonal plane cubic curve that is locally solvable everywhere, but that does not have points over any cubic galois extension of the number field, then the algebraic part of the Brauer-Manin obstruction is not the only obstruction to the Hasse principle for K3 surfaces.
متن کاملMore cubic surfaces violating the Hasse principle
We generalize L. J. Mordell’s construction of cubic surfaces for which the Hasse principle fails.
متن کاملRational Points on Intersections of Cubic and Quadric Hypersurfaces
We investigate the Hasse principle for complete intersections cut out by a quadric and cubic hypersurface defined over the rational numbers.
متن کاملRATIONAL POINTS ON CUBIC HYPERSURFACES OVER Fq(t)
The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field Fq(t), provided that char(Fq) > 3 and X has dimension at least 6.
متن کامل