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The Generalized Polynomial Goldbach Problem

✍ Scribed by Mireille Car

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 1003 KB
Volume: 57
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.1996.0032

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✦ Synopsis

In this paper, we are interested by the following generalization for the polynomial Goldbach problem. Let A 1 , A 2 , and A 3 be coprime polynomials in the ring F q [T]. We ask the question of the representation of a polynomial M # F q [T ] as a sum

where P 1 , P 2 , P 3 are irreducible polynomials subjected to verify some degree conditions. Using the circle method, we get asymptotic estimates for the number of these representations.

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