On the pairwise maxima of generalised divisor functions
Bueno De Andrade, J
Quarterly Journal of Mathematics
Oxford University Press (OUP)
© The Author(s) 2018. Published by Oxford University Press. All rights reserved.
Reason for embargo
Under embargo until 02 March 2019 in compliance with publisher policy.
In this paper, we prove the asymptotic growth rate of the summatory function of the pairwise maxima of the generalised divisor function dk(n), for a fixed positive integer k ≥ 2. This result generalises previous results of Katai, Erdos and Hall on the local behaviour of divisor function on short intervals.
The first author is grateful to the Leverhulme Trust (RPG-2017-320) for the support through the research grant “Moments of L-functions in Function Fields and Random Matrix Theory”.
This is the author accepted manuscript. The final version is available from Oxford University Press (OUP) via the DOI in this record.
Published online 02 March 2018.