Quadratic equations over p-adic fields and their applications in statistical mechanics

The p-adic models of statistical mechanics require the investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to the classic domains not. This quest...

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Main Authors:	Saburov, Mansoor, Ahmad, Mohd Ali Khameini
Format:	Article
Language:	English
Published:	Thailands National Science & Technology Development Agency 2015
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/1/Quadratic_Equation_---_SA.pdf

id	iium-45055
recordtype	eprints
spelling	iium-450552017-08-16T04:27:39Z http://irep.iium.edu.my/45055/ Quadratic equations over p-adic fields and their applications in statistical mechanics Saburov, Mansoor Ahmad, Mohd Ali Khameini QA Mathematics The p-adic models of statistical mechanics require the investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to the classic domains not. This question was open even for a quadratic equation. In this paper, by using the Newton polygon, we provide solvability criteria for quadratic equations over the domains mentioned above for all odd primes p. We also study the number of roots of quadratic equations over all domains given above. This study allows us to present a local description of roots of quadratic equations over p-adic fields whenever p > 2. Thailands National Science & Technology Development Agency 2015 Article PeerReviewed application/pdf en http://irep.iium.edu.my/45055/1/Quadratic_Equation_---_SA.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini (2015) Quadratic equations over p-adic fields and their applications in statistical mechanics. ScienceAsia, 41 (3). pp. 209-215. ISSN 1513-1874 http://www.scienceasia.org/content/content.php?v=36
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Quadratic equations over p-adic fields and their applications in statistical mechanics
description	The p-adic models of statistical mechanics require the investigation of the roots of polynomial equations over p-adic fields in order to construct p-adic Gibbs measures. The most frequently asked question is that whether a root of a polynomial equation belongs to the classic domains not. This question was open even for a quadratic equation. In this paper, by using the Newton polygon, we provide solvability criteria for quadratic equations over the domains mentioned above for all odd primes p. We also study the number of roots of quadratic equations over all domains given above. This study allows us to present a local description of roots of quadratic equations over p-adic fields whenever p > 2.
format	Article
author	Saburov, Mansoor Ahmad, Mohd Ali Khameini
author_facet	Saburov, Mansoor Ahmad, Mohd Ali Khameini
author_sort	Saburov, Mansoor
title	Quadratic equations over p-adic fields and their applications in statistical mechanics
title_short	Quadratic equations over p-adic fields and their applications in statistical mechanics
title_full	Quadratic equations over p-adic fields and their applications in statistical mechanics
title_fullStr	Quadratic equations over p-adic fields and their applications in statistical mechanics
title_full_unstemmed	Quadratic equations over p-adic fields and their applications in statistical mechanics
title_sort	quadratic equations over p-adic fields and their applications in statistical mechanics
publisher	Thailands National Science & Technology Development Agency
publishDate	2015
url	http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/1/Quadratic_Equation_---_SA.pdf
first_indexed	2023-09-18T21:04:05Z
last_indexed	2023-09-18T21:04:05Z
_version_	1777410816713162752

Quadratic equations over p-adic fields and their applications in statistical mechanics

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