Publication: On Montgomery's conjecture and the distribution of Dirichlet sums
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Publication Date
2014-08
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Elsevier
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Abstract
A new version of Montgomery's conjecture (1971) on the estimation of Dirichlet sums is disproved by means of a modification of the idea of "short sums" (due to Bourgain, 1991). We also study the distribution of the values of Dirichlet's "long sums".