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The circle method and pairs of quadratic forms

Henryk Iwaniec, Ritabrata Munshi (2010)

Journal de Théorie des Nombres de Bordeaux

We give non-trivial upper bounds for the number of integral solutions, of given size, of a system of two quadratic form equations in five variables.

The u-invariant of fields with 16 and 32 square classes I

Bronisława Błaszczyk (1980)

Annales Polonici Mathematici

We discuss here the conjectures of Kaplansky and of Lam concerning the ii-univariant of a field of characteristic different from two. Both conjectures are shown t.o hold true for any field having at most 32 square classes.

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