Brauer's Theorem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Brauer''s theorem, named for Richard Brauer, is a result on the representability of 0 by forms over certain fields in sufficiently many variables.One can show that if n is sufficiently large according to the above corollary, then n is greater than r2. Indeed, Emil Artin conjectured that every homogeneous polynomial of degree r over Qp in more than r2 variables represents 0. This is obviously true for r=1, and it is well-known that the conjecture is…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, Brauer''s theorem, named for Richard Brauer, is a result on the representability of 0 by forms over certain fields in sufficiently many variables.One can show that if n is sufficiently large according to the above corollary, then n is greater than r2. Indeed, Emil Artin conjectured that every homogeneous polynomial of degree r over Qp in more than r2 variables represents 0. This is obviously true for r=1, and it is well-known that the conjecture is true for r = 2 (see, for example, J.-P. Serre, A Course in Arithmetic, Chapter IV, Theorem 6). See quasi-algebraic closure for further context.