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- Title
THE EXCEPTIONAL SET IN THE POLYNOMIAL GOLDBACH PROBLEM.
- Authors
POLLACK, PAUL
- Abstract
For each natural number N, let R(N) denote the number of representations of N as a sum of two primes. Hardy and Littlewood proposed a plausible asymptotic formula for R(2N) and showed, under the assumption of the Riemann Hypothesis for Dirichlet L-functions, that the formula holds "on average" in a certain sense. From this they deduced (under ERH) that all but Oϵ(x1/2+ϵ) of the even natural numbers in [1, x] can be written as a sum of two primes. We generalize their results to the setting of polynomials over a finite field. Owing to Weil's Riemann Hypothesis, our results are unconditional.
- Subjects
SET theory; POLYNOMIALS; NATURAL numbers; MATHEMATICAL formulas; RIEMANN hypothesis; FINITE fields; GOLDBACH conjecture
- Publication
International Journal of Number Theory, 2011, Vol 7, Issue 3, p579
- ISSN
1793-0421
- Publication type
Article
- DOI
10.1142/S1793042111004423