File:Mangoldt-series.svg

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Original file(SVG file, nominally 600 × 480 pixels, file size: 13 KB)

Summary[edit]

Description
English: Graph of a series involving the von Mangoldt function. More precisely, this is a graph of the function

considered by Hardy and Littlewood in 1916. They demonstrated that

Curiously, they also show that this function is oscillatory as well, with diverging oscillations. In particular, there exists a value such that

and
infinitely often. This graph demonstrates that the second condition is not immediately apparent, numerically. The graph of this function appears to be remarkably linear in the region and visually appears to have an intercept with the y-axis at about -0.337877. However, on closer examination, one discovers oscillations of increasing magnitude as the function approaches . For the oscillations shown in this graph, a summation including more than 2 billion terms of the series was required.
Date 3 July 2006; (original upload date)
Source Own work
Author Linas Vepstas (User:Linas)

Licensing[edit]

GNU head 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.
w:en:Creative Commons
attribution share alike
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This licensing tag was added to this file as part of the GFDL licensing update.

Original upload log[edit]

Transferred from en.wikipedia to Commons using For the Common Good.

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
15:19, 4 July 2006 600 × 480 (12,300 bytes) w:en:Linas (talk | contribs) higher precision, 2 billion terms
04:40, 4 July 2006 600 × 480 (9,078 bytes) w:en:Linas (talk | contribs) oops, its upside-down
04:14, 4 July 2006 600 × 480 (9,080 bytes) w:en:Linas (talk | contribs) Graph of a series involving the [[von Mangoldt function]]. Created by Linas Vepstas [[User:Linas]] on 3 July 2006

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current17:40, 25 October 2015Thumbnail for version as of 17:40, 25 October 2015600 × 480 (13 KB)Pqnlrn (talk | contribs)Reverted to version as of 18:30, 2 November 2013 (UTC)
17:39, 25 October 2015Thumbnail for version as of 17:39, 25 October 2015600 × 420 (49 KB)Pqnlrn (talk | contribs)Rewrote the ordinate axis label in graphical form
18:30, 2 November 2013Thumbnail for version as of 18:30, 2 November 2013600 × 480 (13 KB)McPot (talk | contribs)Trying to fix broken SVG-thumbnail. [inkscape --export-plain-svg] (Uploaded new version of file using Wiki.java)
15:13, 16 October 2013No thumbnail0 × 0 (12 KB)OgreBot (talk | contribs)(BOT): Reverting to most recent version before archival
15:12, 16 October 2013No thumbnail0 × 0 (9 KB)OgreBot (talk | contribs)(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2006-07-04 04:40:04 by Linas
15:12, 16 October 2013No thumbnail0 × 0 (9 KB)OgreBot (talk | contribs)(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2006-07-04 04:14:52 by Linas
16:04, 3 September 2013No thumbnail0 × 0 (12 KB)Clarkcj12 (talk | contribs)Transferred from en.wikipedia: see original upload log above
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