number theory seminar this Thursday, March 8 at 3:35pm
William Stein
There will be a number theory seminar this Thursday, March 8 at 3:35pm.
TITLE: Linearly Irregular Primes- A first report
SPEAKERS: Alyson Deines and Ben Lundell
LOCATION: 3:35 in Padelford C401 on March 8, 2012
ABSTRACT:
A prime number $p$ is called irregular if $p$ divides the class number
of the $p$-th cyclotomic field. Through work of Kummer,
Kubota-Leopoldt, and Iwasawa, this irregularity condition is related
to the $p$-divisibility of certain Bernoulli numbers, which themselves
arise as the constant terms of $p$-adic $L$-functions. In this talk,
we'll explain these ideas and how to extend them to relate congruences
of Bernoulli numbers modulo $p^2$ to the $p$-divisibility of the
linear term of the $p$-adic $L$-function. We will also explain how to
efficiently compute these congruences and provide some preliminary
computational evidence which suggests a definite pattern.
http://wiki.wstein.org/seminar/nt/20120308
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William Stein
Professor of Mathematics
University of Washington
http://wstein.org