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 tru...
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.
