Liouville-log.svg
Summary
Description Liouville-log.svg |
Logarithmic-scale graph of the summatory en:Liouville function . That is, this is a graph of for . The summatory function is graphed in red. The green spike indicates the location where the en:Pólya conjecture fails. The Pólya conjecture fails to hold for most values of in the region of . In this region, the function reaches a maximum value of 829 at , which is represented by the height of the green bar. The blue line indicates the contribution of the first non-trivial zero of the Riemann zeta function to the summatory Liouville function. Specifically, the blue line shows Here, denotes the en:absolute value . The only reason for taking the max of 0.3 or the sine function is to avoid cluttering the image. The first non-trivial zero of the Riemann zeta function is located at |
Date | 4 June 2007 (original upload date) |
Source | Original uploaded on en.wikipedia (transferred to commons by Hagman ) |
Author | Created by Linas Vepstas en:User:Linas |
References
- ↑ Philippe Flajolet, Linas Vepstas, "On Differences of Zeta Values", arXiv math/0611332
Licensing
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License , Version 1.2 or any later version published by the Free Software Foundation ; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License . http://www.gnu.org/copyleft/fdl.html GFDL GNU Free Documentation License true true |
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
Attribution: Linas at the English Wikipedia | ||
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This licensing tag was added to this file as part of the GFDL licensing update . http://creativecommons.org/licenses/by-sa/3.0/ CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 true true |
Original upload log
Upload date | User | Bytes | Dimensions | Comment
- 2007-06-04 02:49:18 | Linas | 27093 | 600×480 | Created by Linas Vepstas [[User:Linas]] 3 June 2007