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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rosen, M. (2002). The Class Number Formulas in Quadratic and Cyclotomic Function Fields. In: Number Theory in Function Fields. Graduate Texts in Mathematics, vol 210. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6046-0_16
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6046-0_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2954-9
Online ISBN: 978-1-4757-6046-0
eBook Packages: Springer Book Archive