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. 
@article{10_4064_aa167_3_6,
     author = {Franti\v{s}ek Marko},
     title = {Congruences of {Ankeny{\textendash}Artin{\textendash}Chowla} type and
 the $p$-adic class number formula revisited},
     journal = {Acta Arithmetica},
     pages = {281--298},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2015},
     doi = {10.4064/aa167-3-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa167-3-6/}
}
TY  - JOUR
AU  - František Marko
TI  - Congruences of Ankeny–Artin–Chowla type and
 the $p$-adic class number formula revisited
JO  - Acta Arithmetica
PY  - 2015
SP  - 281
EP  - 298
VL  - 167
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa167-3-6/
DO  - 10.4064/aa167-3-6
LA  - en
ID  - 10_4064_aa167_3_6
ER  - 
%0 Journal Article
%A František Marko
%T Congruences of Ankeny–Artin–Chowla type and
 the $p$-adic class number formula revisited
%J Acta Arithmetica
%D 2015
%P 281-298
%V 167
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa167-3-6/
%R 10.4064/aa167-3-6
%G en
%F 10_4064_aa167_3_6
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. http://geodesic.mathdoc.fr/articles/10.4064/aa167-3-6/

Cité par Sources :