# Decomposition of congruences involving a map $Φ$

In: Mathematica Slovaca, vol. 60, no. 6
František Marko
Detaily:
Rok, strany: 2010, 793 - 800
Kľúčové slová:
Bernoulli numbers, class number, Ankeny-Artin-Chowla congruence
O článku:
Congruences of Ankeny-Artin-Chowla type modulo $p2$ for a cyclic subfield $K$ of prime conductor $p$ were derived by Jakubec and expressed in terms of a technically defined map $Φ$. Later, Jakubec and Lassak found a decomposition of the map $Φ$ modulo $p2$ and simplified the formulation of these congruences. A corresponding decomposition of the map $Φ$ modulo $p3$ was obtained in [MARKO, F.:\textit{Towards Ankeny-Artin-Chowla type congruence modulo $p3$}, Ann. Math. Sil. \textbf{20} (2006), 31–55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo $p3$. This paper will show how to produce an analogous decomposition of the map $Φ$ modulo an arbitrary power $pn$ which would allow a description of analogous congruences modulo $pn$.
Ako citovať:
ISO 690:
Marko, F. 2010. Decomposition of congruences involving a map $Φ$. In Mathematica Slovaca, vol. 60, no.6, pp. 793-800. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0047-1

APA:
Marko, F. (2010). Decomposition of congruences involving a map $Φ$. Mathematica Slovaca, 60(6), 793-800. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0047-1
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