2000 •
Congruences among the Values of 2-Adic L-Functions
Authors:
Jerzy Urbanowicz, Kenneth S. Williams
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 Wojcik, 1995/1996] and [Wojcik, 1998]. This chapter will focus on the results given in the latter three pa (...)
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 Wojcik, 1995/1996] and [Wojcik, 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. (Read More)
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