Algebraic $K$-theory and sums-of-squares formulas
Copyright policy )Algebraic $K$-theory and sums-of-squares formulas
We prove a result about the existence of certain 'sums-of-squares' formulas over a field F . A classical theorem uses topological K -theory to show that if such a formula exists over \mathbb R , then certain powers of 2 must divide certain binomial coefficients. In this paper we use algebraic K -theory to extend the result to all fields not of characteristic 2.
General binary quadratic forms, Rings and Algebras (math.RA), FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Mathematics - Rings and Algebras, \(K\)-theory in number theory, Quadratic forms over general fields, Sum of squares
General binary quadratic forms, Rings and Algebras (math.RA), FOS: Mathematics, Algebraic Topology (math.AT), Mathematics - Algebraic Topology, Mathematics - Rings and Algebras, \(K\)-theory in number theory, Quadratic forms over general fields, Sum of squares
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