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

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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 pt and to equalities in the p-adic completion double-struck Qp of the field of rational numbers double-struck Q. Additional connections to the Gross-Koblitz formula and explicit congruences for quadratic and cubic fields are given.

Original languageEnglish (US)
Pages (from-to)281-298
Number of pages18
JournalActa Arithmetica
Volume167
Issue number3
DOIs
StatePublished - Jan 1 2015

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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