Geodesic
Congruences of Ankeny–Artin–Chowla type and the $p$-adic class number formula revisited
František Marko1
1 Pennsylvania State University 76 University Drive Hazleton, PA 18202, U.S.A.
Acta Arithmetica, Tome 167 (2015) no. 3, pp. 281-298

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 ${\mathbb {Q}_p}$ of the field of rational numbers $\mathbb {Q}$. Additional connections to the Gross–Koblitz formula and explicit congruences for quadratic and cubic fields are given.
DOI : 10.4064/aa167-3-6
Keywords: purpose paper interpret results jakubec his collaborators congruences ankeny artin chowla type cyclic totally real fields elementary algebraic version p adic class number formula modulo powers generalize previous results congruences modulo arbitrary powers equalities p adic completion mathbb field rational numbers mathbb additional connections gross koblitz formula explicit congruences quadratic cubic fields given

František Marko 1

1 Pennsylvania State University 76 University Drive Hazleton, PA 18202, U.S.A. 
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 the $p$-adic class number formula revisited},
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 the $p$-adic class number formula revisited
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František Marko. Congruences of Ankeny–Artin–Chowla type and
 the $p$-adic class number formula revisited. Acta Arithmetica, Tome 167 (2015) no. 3, pp. 281-298. doi: 10.4064/aa167-3-6

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