Sandro Bettin, J. Brian Conrey
Published 2020-02-21Version 1
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.
Comments: 20 pages, 2 figures
Non-vanishing of Dirichlet series with periodic coefficients
On an asymptotic behavior of the divisor function $τ(n)$
On Karatsuba's Problem Concerning the Divisor Function $τ(n)$
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