Averages of long Dirichlet polynomials
Sandro Bettin, J. Brian Conrey
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Abstract
We consider the asymptotic behavior of the mean square of truncations of the Dirichlet series of . We discuss the connections of this problem with that of the variance of the divisor function in short intervals and in arithmetic progressions, reviewing the recent results on this topic. Finally, we show how these results can all be proved assuming a suitable version of the moments conjecture.
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Taxonomy
TopicsAnalytic Number Theory Research · Meromorphic and Entire Functions · Advanced Mathematical Identities