Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited

• Autorzy: František Marko
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to interpret the results of Jakubec and his collaborators on congruences of Ankeny-Artin-Chowla type for cyclic totally real fields as an elementary algebraic version of the p-adic class number formula modulo powers of p. We show how to generalize the previous results to congruences modulo arbitrary powers $p^t$ and to equalities in the p-adic completion $ℚ_p$ of the field of rational numbers ℚ. Additional connections to the Gross-Koblitz formula and explicit congruences for quadratic and cubic fields are given.

Kategorie tematyczne

• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 167
• Numer: 3
• Strony: 281-298

Daty

wydano

2015

Twórcy

autor

František Marko

• Pennsylvania State University, 76 University Drive, Hazleton, PA 18202, U.S.A.

Identyfikatory

DOI

10.4064/aa167-3-6