Subject: Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert
From: Emili Bifet (bifet@attglobal.net)
Date: Sat Mar 18 2000 - 17:32:32 EST
Dear Andrew,
it was late last night when I wrote my message. This morning, when I
read it again, the last sentence felt misleading. This expresses
better what I meant:
This centrality [of the RH] should not be too surprising, after all
the zeta function encodes all the information about how integers are
built out of prime numbers; and let us not forget that its zeroes are,
in a certain sense, essentially related to those prime numbers ...
By the way, if you follow the third link in David Wilkins' page
http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/
you will end up at
http://mathworld.wolfram.com/RiemannHypothesis.html
Once there, please be aware that Artin's Conjecture refers to Function
Fields (e.g. the field of rational functions over a finite field)
rather than Number Fields. It is also called the Riemann Hypothesis
because of a powerful analogy that exists between the two contexts.
One striking difference though, is that Artin's Conjecture has been an
expanding theorem throughout the 20th Century, whereas we still don't
know how to prove Riemann's original Hypothesis.
Overall, I would recommend Daniel Bump's site
as being the one closer to current research.
Best wishes,
Emili Bifet
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