Decomposition of congruences involving a map Φ

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Congruences of Ankeny-Artin-Chowla type modulo p 2 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 p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.

Original languageEnglish (US)
Pages (from-to)793-800
Number of pages8
JournalMathematica Slovaca
Volume60
Issue number6
DOIs
StatePublished - Dec 1 2010

Fingerprint

Congruence
Modulo
Decompose
Formulation
Subfield
Conductor
Arbitrary

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{b2b1d38ec3a84e25a3bb79da5c6932f7,
title = "Decomposition of congruences involving a map Φ",
abstract = "Congruences of Ankeny-Artin-Chowla type modulo p 2 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 p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.",
author = "František Marko",
year = "2010",
month = "12",
day = "1",
doi = "10.2478/s12175-010-0047-1",
language = "English (US)",
volume = "60",
pages = "793--800",
journal = "Mathematica Slovaca",
issn = "0139-9918",
publisher = "Versita",
number = "6",

}

Decomposition of congruences involving a map Φ. / Marko, František.

In: Mathematica Slovaca, Vol. 60, No. 6, 01.12.2010, p. 793-800.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Decomposition of congruences involving a map Φ

AU - Marko, František

PY - 2010/12/1

Y1 - 2010/12/1

N2 - Congruences of Ankeny-Artin-Chowla type modulo p 2 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 p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.

AB - Congruences of Ankeny-Artin-Chowla type modulo p 2 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 p 2 and simplified the formulation of these congruences. A corresponding decomposition of the map Φ modulo p 3 was obtained in [MARKO, F.: Towards Ankeny-Artin-Chowla type congruence modulo p 3, Ann. Math. Sil. 20 (2006), 31-55]. That technical step was important for the formulation of congruences of Ankeny-Artin-Chowla type modulo p 3. This paper will show how to produce an analogous decomposition of the map Φ modulo an arbitrary power p n which would allow a description of analogous congruences modulo p n.

UR - http://www.scopus.com/inward/record.url?scp=78650248027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650248027&partnerID=8YFLogxK

U2 - 10.2478/s12175-010-0047-1

DO - 10.2478/s12175-010-0047-1

M3 - Article

VL - 60

SP - 793

EP - 800

JO - Mathematica Slovaca

JF - Mathematica Slovaca

SN - 0139-9918

IS - 6

ER -