Gunns, Jos and Hughes, Christopher Paul orcid.org/0000-0002-7649-3548 (2019) The effect of repeated differentiation on L-functions. Journal of Number Theory. pp. 30-43. ISSN: 0022-314X
Abstract
We show that under repeated differentiation, the zeros of the Selberg $\Xi$-function become more evenly spaced out, but with some scaling towards the origin. We do this by showing the high derivatives of the $\Xi$-function converge to the cosine function, and this is achieved by expressing a product of Gamma functions as a single Fourier transform.
Metadata
| Item Type: | Article |
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| Authors/Creators: |
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| Copyright, Publisher and Additional Information: | © 2018 Elsevier Inc. All rights reserved. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. |
| Dates: |
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| Institution: | The University of York |
| Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
| Depositing User: | Pure (York) |
| Date Deposited: | 24 Aug 2018 08:00 |
| Last Modified: | 20 Sep 2025 00:40 |
| Published Version: | https://doi.org/10.1016/j.jnt.2018.07.008 |
| Status: | Published |
| Refereed: | Yes |
| Identification Number: | 10.1016/j.jnt.2018.07.008 |
| Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:134951 |
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