Averages of long Dirichlet polynomials

Abstract

We consider the asymptotic behavior of the mean square of truncations of the Dirichlet series of $\zeta (s{)}^k$. 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.

arXiv comment21 pages, 2 figures, minor modifications

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Cited by in corpus (1)

• A combinatorial identity and the finite dual of infinite dihedral group algebra