Some Numerical Implications of the Hardy and Littlewood Analysis of the 3-Primes Problem

Author: Effinger, G.

Source: The Ramanujan Journal, Volume 3, Number 3, 1 September 1999 , pp. 239-280(42)

Publisher: Springer

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Abstract:

We explore some of the numerical implications of the famous 1922 paper “Some Problems of ‘Partitio Numerorum’; III: On the Expression of a Number as a Sum of Primes” of Hardy and Littlewood. In particular, we prove that if the Generalized Riemann Hypothesis holds, then Hardy and Littlewood's analysis yields that every odd number greater than 1.24 × 10^50 is a sum of three primes.

Keywords: 3-primes problem; Hardy and Littlewood; additive number theory; circle method; numerics; vinogradov

Document Type: Regular Paper

Affiliations: Department of Mathematics and Computer Science, Skidmore College, Saratoga Springs, NY 12866. effinger@skidmore.edu

Publication date: September 1, 1999

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