The study on general cubic equations over p-adic fields

A Diophantine problem means to find all solutions of an equation or system of equations in integers, rational numbers, or sometimes more general number rings. The most frequently asked question is whether a root of a polynomial equation with coefficients in a p-adic field ℚp belongs to domains ℤ∗p,...

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Main Authors:	Saburov, Mansoor, Ahmad, Mohd Ali Khameini, Alp, Murat
Format:	Article
Language:	English
Published:	University of Nis 2021
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/94792/1/MohdAliKhameini2021_TheStudyonGeneralCubic.pdf http://eprints.utm.my/id/eprint/94792/ http://dx.doi.org/10.2298/FIL2104115S
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Institution:	Universiti Teknologi Malaysia
Language:	English

id	my.utm.94792
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spelling	my.utm.947922022-04-29T22:26:59Z http://eprints.utm.my/id/eprint/94792/ The study on general cubic equations over p-adic fields Saburov, Mansoor Ahmad, Mohd Ali Khameini Alp, Murat QA Mathematics A Diophantine problem means to find all solutions of an equation or system of equations in integers, rational numbers, or sometimes more general number rings. The most frequently asked question is whether a root of a polynomial equation with coefficients in a p-adic field ℚp belongs to domains ℤ∗p, ℤp \ ℤ∗p, ℚp \ ℤp, ℚp or not. This question is open even for lower degree polynomial equations. In this paper, this problem is studied for cubic equations in a general form. The solvability criteria and the number of roots of the general cubic equation over the mentioned domains are provided. University of Nis 2021-11 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/94792/1/MohdAliKhameini2021_TheStudyonGeneralCubic.pdf Saburov, Mansoor and Ahmad, Mohd Ali Khameini and Alp, Murat (2021) The study on general cubic equations over p-adic fields. Filomat, 35 (4). pp. 1115-1131. ISSN 0354-5180 http://dx.doi.org/10.2298/FIL2104115S DOI:10.2298/FIL2104115S
institution	Universiti Teknologi Malaysia
building	UTM Library
collection	Institutional Repository
continent	Asia
country	Malaysia
content_provider	Universiti Teknologi Malaysia
content_source	UTM Institutional Repository
url_provider	http://eprints.utm.my/
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Alp, Murat The study on general cubic equations over p-adic fields
description	A Diophantine problem means to find all solutions of an equation or system of equations in integers, rational numbers, or sometimes more general number rings. The most frequently asked question is whether a root of a polynomial equation with coefficients in a p-adic field ℚp belongs to domains ℤ∗p, ℤp \ ℤ∗p, ℚp \ ℤp, ℚp or not. This question is open even for lower degree polynomial equations. In this paper, this problem is studied for cubic equations in a general form. The solvability criteria and the number of roots of the general cubic equation over the mentioned domains are provided.
format	Article
author	Saburov, Mansoor Ahmad, Mohd Ali Khameini Alp, Murat
author_facet	Saburov, Mansoor Ahmad, Mohd Ali Khameini Alp, Murat
author_sort	Saburov, Mansoor
title	The study on general cubic equations over p-adic fields
title_short	The study on general cubic equations over p-adic fields
title_full	The study on general cubic equations over p-adic fields
title_fullStr	The study on general cubic equations over p-adic fields
title_full_unstemmed	The study on general cubic equations over p-adic fields
title_sort	study on general cubic equations over p-adic fields
publisher	University of Nis
publishDate	2021
url	http://eprints.utm.my/id/eprint/94792/1/MohdAliKhameini2021_TheStudyonGeneralCubic.pdf http://eprints.utm.my/id/eprint/94792/ http://dx.doi.org/10.2298/FIL2104115S
_version_	1732945394662375424

The study on general cubic equations over p-adic fields

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