From: greg@math.ucdavis.edu (Greg Kuperberg)
Subject: This week in the mathematics arXiv (7 Aug - 11 Aug)
Date: 15 Aug 2000 15:17:07 -0700
Newsgroups: sci.math.research
Summary: [missing]

[deletia --djr]

Tanguy Rivoal contributed a result which was announced recently in
sci.math.research, that the dimension of the rational span of zeta(2),
... , zeta(n) grows at least logarithmically in n [math.NT/0008051]. This
immediately implies that infinitely many integer zeta values are
irrational.  I don't know French, and my number theory is hardly better,
but it appears to be one of those elementary irrationality arguments
that is far easier to understand than to find.  (For example there
is a slick proof, possibly due to Niven, that pi is transcendental.)
It shouldn't take long to check this result.  Has anyone already done so?

I note that the article does not have the superficial indications of
error that I have seen before.  In particular the author does *not*
boast that the proof is much easier than expected, even though the
article is very short. "Things should be made as simple as possible --
but no simpler." - Einstein

"This week in the mathematics archive" may be freely redistributed
with attribution and without modification.

[deletia --djr]

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