Sums of Squares in Function Fields of Quadrics and Conics
نویسنده
چکیده
For a quadric Q over a real field k, we investigate whether finiteness of the Pythagoras number of the function field k(Q) implies the existence of a uniform bound on the Pythagoras numbers of all finite extensions of k. We give a positive answer if the quadratic form that defines Q is weakly isotropic. In the case where Q is a conic, we show that the Pythagoras number of k(Q) is 2 only if k is hereditarily pythagorean.
منابع مشابه
Sums of Three Squares in Function Fields of Conics and Cassels–catalan Curves
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