Expansion and Improvement of Sieve and application in Goldbach's problem

Details Expansion and Improvement of Sieve and application in Goldbach's problem Expansion and Improvement of Sieve and application in Goldbach's problem

2009-04-22

arxiv.org/abs/0904.3365v1

Mathematics

Number Theory

50 pages, 5 tables

Scientific paper

This paper expands and improves on the general Sieve method. This expaned and
improved Sieve is applied to Goldbach's problem. A new estimate of the
exception set in Goldbach's number E(X), an improved lower bound D_{1,2}(N) and
upper bound D(N) are proposed. The proposed values are: |E(X)|<= X^{0.702+e},
D_{1,2}(N)>= 2.27C(N)/ln^{2}(N), D(N) <= 6.916C(N)/ln^{2}(N).

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