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 and to equalities in the p-adic completion of the field of rational numbers ℚ. Additional connections to the Gross-Koblitz formula and explicit congruences for quadratic and cubic fields are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-6,
author = {Franti\v sek Marko},
title = {Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {281-298},
zbl = {1317.11111},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-6}
}
František Marko. Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited. Acta Arithmetica, Tome 168 (2015) pp. 281-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-3-6/