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The Three Primes Theorem with Almost Equal Summands

R. C. Baker and G. Harman
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 356, No. 1738, Applications of the Hardy-Littlewood Method (Mar. 15, 1998), pp. 763-780
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/54890
Page Count: 18
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The Three Primes Theorem with Almost Equal Summands
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Abstract

The problem of representing all sufficiently large odd numbers as the sum of three nearly equal primes is tackled using the Hardy-Littlewood circle method in tandem with a sieve method. A combination of the Harman and vector sieves, as developed by Baker, Harman and Pintz, is used. To do this, the major arcs of the circle method involve the investigation of the mean-values of Dirichlet polynomials, while the minor arcs demand short-range estimates for exponential sums.

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