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A lower bound for the variance of generalized divisor functions in arithmetic progressions
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Mastrostefano, Daniele (2022) A lower bound for the variance of generalized divisor functions in arithmetic progressions. The Ramanujan Journal, 57 . pp. 623-695. doi:10.1007/s11139-020-00374-8 ISSN 1382-4090.
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Official URL: http://dx.doi.org/10.1007/s11139-020-00374-8
Abstract
We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a result for any α-fold divisor function, for any complex number α∉{1}∪−N, even when considering a sequence of parameters α close in a proper way to 1. Our work builds on that of Harper and Soundararajan, who handled the particular case of k-fold divisor functions dk(n), with k∈N≥2.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Number theory, Arithmetic functions, Combinatorial analysis, Series, Arithmetic, Divisor theory | ||||||||
| Journal or Publication Title: | The Ramanujan Journal | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 1382-4090 | ||||||||
| Official Date: | February 2022 | ||||||||
| Dates: |
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| Volume: | 57 | ||||||||
| Page Range: | pp. 623-695 | ||||||||
| DOI: | 10.1007/s11139-020-00374-8 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 23 June 2021 | ||||||||
| Date of first compliant Open Access: | 24 June 2021 | ||||||||
| RIOXX Funder/Project Grant: |
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