Subject: Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert
From: Emili Bifet (bifet@attglobal.net)
Date: Sat Mar 18 2000 - 00:59:49 EST
Dear Andrew,
concerning the Riemann Hypothesis, you may want to have a look at the
original source:
http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/
The three links that appear there will provide you with information
about what progress ...
There are also two recent papers that may be useful:
Zeroes of zeta functions and symmetry
Author(s): Nicholas M. Katz; Peter Sarnak.
Journal: Bull. Amer. Math. Soc. 36 (1999), 1-26.
http://www.ams.org/bull/1999-36-01/S0273-0979-99-00766-1/S0273-0979-99-00766-1.pdf
Noncommutative Geometry and the Riemann Zeta Function
Author: Alain Connes.
http://www.math.ohio-state.edu/connes/zeta2.pdf
http://www.math.ohio-state.edu/connes/Connes_course.html
As to its significance: a proof of the Riemann Hypothesis would change
the Geography of Number Theory. (Think of the Montblanc in the Alps:
monumental in its presence and a huge obstacle any time you try to go
anywhere.) There are many difficult and important results, the prime
number theorem for one, that become much easier once the Riemann
Hypothesis is assumed. This 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 those prime numbers ...
Best wishes,
Emili Bifet
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