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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.

2013-05-11 18:34