Improvements in Birch’s Theorem on Forms in Many Variables
نویسنده
چکیده
We show that a non-singular integral form of degree d is soluble over the integers if and only if it is soluble over R and over Qp for all primes p, provided that the form has at least (d− 12 √ d)2 variables. This improves on a longstanding result of Birch.
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