In this paper we will study the distribution of Hardy-Littlewood numbers in short intervals both unconditionally and conditionally, \emph{i.e.} assuming the Riemann Hypothesis (RH). Our results concern the average of the asymptotic formula for the number of representations of an HL-number in almost all short intervals.
On the Hardy-Littlewood problem in short intervals
LANGUASCO, ALESSANDRO;
2008
Abstract
In this paper we will study the distribution of Hardy-Littlewood numbers in short intervals both unconditionally and conditionally, \emph{i.e.} assuming the Riemann Hypothesis (RH). Our results concern the average of the asymptotic formula for the number of representations of an HL-number in almost all short intervals.
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