منابع مشابه
The Hasse Principle for Pairs of Diagonal Cubic Forms
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.
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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 کاملON THE h-INVARIANT OF CUBIC FORMS, AND SYSTEMS OF CUBIC FORMS
We define a so-called `-invariant for systems of homogeneous forms of the same degree, which coincides with the well known h-invariant for a single quadratic or cubic form, and bound the `-invariant of a system of rational forms F1, . . . , Fr in terms of the `-invariant of a single form α1F1 + . . . + αrFr in their complex pencil in case of algebraic α1, . . . , αr. As an application, we show ...
متن کاملOn Systems of Diagonal Forms
In this paper we consider systems of diagonal forms with integer coefficients in which each form has a different degree. Every such system has a nontrivial zero in every p-adic field Qp provided that the number of variables is sufficiently large in terms of the degrees. While the number of variables required grows at least exponentially as the degrees and number of forms increase, it is known t...
متن کاملOn the Smallest Point on a Diagonal Cubic Surface
For diagonal cubic surfaces, we study the behaviour of the height of the smallest rational point versus the Tamagawa type number introduced by E. Peyre.
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ژورنال
عنوان ژورنال: Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 1998
ISSN: 1364-503X,1471-2962
DOI: 10.1098/rsta.1998.0181