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

František Marko

Acta Arithmetica (2015)

  • Volume: 167, Issue: 3, page 281-298
  • ISSN: 0065-1036

Abstract

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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.

How to cite

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František Marko. "Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited." Acta Arithmetica 167.3 (2015): 281-298. <http://eudml.org/doc/278855>.

@article{FrantišekMarko2015,
abstract = {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.},
author = {František Marko},
journal = {Acta Arithmetica},
keywords = {Bernoulli numbers; -adic class number formula; Ankeny-Artin-Chowla congruences},
language = {eng},
number = {3},
pages = {281-298},
title = {Congruences of Ankeny-Artin-Chowla type and the p-adic class number formula revisited},
url = {http://eudml.org/doc/278855},
volume = {167},
year = {2015},
}

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
VL - 167
IS - 3
SP - 281
EP - 298
AB - 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.
LA - eng
KW - Bernoulli numbers; -adic class number formula; Ankeny-Artin-Chowla congruences
UR - http://eudml.org/doc/278855
ER -

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