Congruences among the Values of 2-Adic L-Functions

Abstract

Our purpose in this chapter is to investigate divisibility properties of the values of L-functions attached to quadratic characters at integers, for example, class numbers and the orders of K ₂-groups of the integers of quadratic fields. Making use of 2-adic L-functions we extend the linear congruence relations considered in the previous chapters. Extensions of this type have been considered in [Gras, 1989], [Uehara, 1990], [Urbanowicz and Wójcik, 1995/1996] and [Wójcik, 1998]. This chapter will focus on the results given in the latter three papers. We begin with some notation and basic properties of p-adic numbers and functions, especially p-adic L-functions.