Mersenne primes and class field theory

Nick · 2012-12-29, 14:38

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).

xilman · 2012-12-29, 15:21

Quote:

Originally Posted by Nick

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

a nicol · 2017-04-01, 09:46

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.

Nick · 2017-04-01, 12:09

Quote:

Originally Posted by a nicol

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).

a nicol · 2017-04-01, 16:26

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"

2012-12-29, 14:38	#1
Nick Dec 2012 The Netherlands 2²·11·37 Posts	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).

2017-04-01, 09:46	#3
a nicol Nov 2016 29 Posts	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

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2017-04-01, 16:26	#5
a nicol Nov 2016 29 Posts	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"