mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2012-12-29, 14:38   #1
Nick
 
Nick's Avatar
 
Dec 2012
The Netherlands

23·181 Posts
Default Mersenne primes and class field theory

Bas Jansen's PhD thesis has just been published and is available here:
http://www.math.leidenuniv.nl/scripties/PhDJansen.pdf

Note: although it begins with a summary in Dutch (and ends with a Dutch CV),
the main abstract and body are in English.

Among the main results are a generalization of the 1996 conjecture of George Woltman (proved in 2000 by Gebre-Egziabher).
Nick is online now   Reply With Quote
Old 2012-12-29, 15:21   #2
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

11×919 Posts
Default

Quote:
Originally Posted by Nick View Post
Bas Jansen's PhD thesis has just been published and is available here:
http://www.math.leidenuniv.nl/scripties/PhDJansen.pdf

Note: although it begins with a summary in Dutch (and ends with a Dutch CV),
the main abstract and body are in English.

Among the main results are a generalization of the 1996 conjecture of George Woltman (proved in 2000 by Gebre-Egziabher).
Hi Nick. Welcome aboard.

I took the liberty of moving your post out of the Misc Math. area. As you are new here I guess you didn't realise that "Misc. Math." is a local euphemism for "garbage posted by cranks" and your posting is very much not in that category.

Paul
xilman is online now   Reply With Quote
Old 2017-04-01, 09:46   #3
a nicol
 
Nov 2016

23×3 Posts
Default

Proposition 8 in the summary of Bas Jansen's paper features a triangle constructed inside another triangle. The summary is in Dutch but this seems to be saying that the outer triangle has twice the area of the inner.

Having gone through the rest of the paper I can't work out what this triangle has to do with Mersenne numbers or the Lucas Lehmer test. Can someone help elaborate on the connection here please?

I've attached a clipping of the proposition.
Attached Thumbnails
Click image for larger version

Name:	bas-jansen-triangle.PNG
Views:	71
Size:	80.5 KB
ID:	15863  
a nicol is online now   Reply With Quote
Old 2017-04-01, 12:09   #4
Nick
 
Nick's Avatar
 
Dec 2012
The Netherlands

23×181 Posts
Default

Quote:
Originally Posted by a nicol View Post
Having gone through the rest of the paper I can't work out what this triangle has to do with Mersenne numbers or the Lucas Lehmer test. Can someone help elaborate on the connection here please?
In our culture, the list of propositions accompanying a PhD thesis is something of an academic flourish.
They must demonstate not just depth but also breadth of original thinking.
As such, several will have no connection to the main subject of research, and some may even be whimsical (though the PhD candidate must still be able to defend them).
Nick is online now   Reply With Quote
Old 2017-04-01, 16:26   #5
a nicol
 
Nov 2016

1816 Posts
Default

Interesting! Thank you for the info Nick, I couldn't work out why there were no other apparent references to it.

"These are being accompanied by propositions ('stellingen'). Such propositions (which have survived in Dutch universities to this day) are a set of statements of a scientific nature, the first few of which may be related to the subject of the thesis itself and the rest is usually of a more general nature. The candidate should be prepared to defend these at the promotion ceremony. In the days of the Kapteyn brothers it was also possible to obtain a doctor's degree solely on presenting and defending a set of propositions"
a nicol is online now   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
theory on Mersenne primes ? science_man_88 science_man_88 396 2017-04-15 18:52
Basic Number Theory 11: Gaussian primes Nick Number Theory Discussion Group 0 2016-12-03 11:42
Conjectured Primality Test for Specific Class of Mersenne Numbers primus Miscellaneous Math 1 2014-10-12 09:25
Quantum field theory xilman Science & Technology 85 2010-12-20 21:42
New Class of primes - proving algorithm AntonVrba Math 2 2008-10-06 00:53

All times are UTC. The time now is 21:13.

Mon Oct 19 21:13:24 UTC 2020 up 39 days, 18:24, 1 user, load averages: 1.69, 1.71, 1.86

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

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.
A copy of the license is included in the FAQ.