Applications of Covering Systems of Integers and Goldbach's Conjecture for Monic Polynomials

Applications of Covering Systems of Integers and Goldbach's Conjecture for Monic Polynomials

60 pages· 2007· ISBN 9780549210207
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Let f(x) be a monic polynomial in Z [x] of degree d > 1. We give a proof that the number reals(y) of representations of f(x) as a sum of two irreducible monic polynomials g(x) and h(x) in Z [x], with the coefficients of g( x) and h(x) bounded in absolute value by y, is asymptotic to (2y) d-1.

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