The Class Number Formulas in Quadratic and Cyclotomic Function Fields

Abstract

In this chapter we will discuss the analogues of some fascinating class number formulas which are well known in the case of quadratic and cyclotomic number fields. Some of these go back to the nineteenth century, e.g., the work of Dirichlet and Kummer. More recent contributions are associated with the names of Carlitz, Iwasawa, and Sinnott. We will review some of these results and then formulate and prove a number of analogues in the function field context.KeywordsPrime PowerClass NumberMonic PolynomialQuadratic Number FieldMonic Irreducible PolynomialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.