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 is called irregular if divides the class number of the -th cyclotomic field. Through work of Kummer, Kubota-Leopoldt, and Iwasawa, this irregularity condition is related to the -divisibility of certain Bernoulli numbers, which themselves arise as the constant terms of -adic -functions. In this talk, we'll explain these ideas and how to extend them to relate congruences of Bernoulli numbers modulo to the -divisibility of the linear term of the -adic -function. We will also explain how to efficiently compute these congruences and provide some preliminary computational evidence which suggests a definite pattern.