%0 Journal Article
%T A Comparison of Sufficiency Condtions for the Goldbach and the Twin Primes Conjectures
%A C. J. Mozzochi
%J Advances in Pure Mathematics
%P 157-170
%@ 2160-0384
%D 2014
%I Scientific Research Publishing
%R 10.4236/apm.2014.45021
%X <p>
	<span style=\"text-align:justify;line-height:1.5;font-family:Verdana;\">It is generally known that
under the generalized Riemann hypothesis one could establish the twin primes
conjecture by the circle method, provided one could obtain the estimate </span><em style=\"text-align:justify;line-height:1.5;\"><span style=\"font-family:Verdana;\">o </span></em><span style=\"text-align:justify;line-height:1.5;font-family:Verdana;\">(<em>n</em>log</span><sup style=\"text-align:justify;\"><span style=\"font-family:Verdana;\">-2</span></sup><span style=\"text-align:justify;line-height:1.5;font-family:Verdana;\"><em> n</em>)&nbsp;for the integral of the representation
function over the minor arcs. One of the new results here is that the
assumption of </span><span style=\"font-family:Verdana;\"><em>GRH</em></span><span style=\"text-align:justify;line-height:1.5;font-family:Verdana;\"> can be removed. We compare this and other such
sufficiency results with similar results for the Goldbach conjecture.</span> 
</p>
%K Goldbach Conjecture
%K Twin Primes Conjecture
%K Circle Method
%K Generalized Riemann Hypothesis
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=45613