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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Thailands National Science & Technology Development Agency
2015
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| Online Access: | http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/1/Quadratic_Equation_---_SA.pdf |
| _version_ | 1848782716628107264 |
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| author | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_facet | Saburov, Mansoor Ahmad, Mohd Ali Khameini |
| author_sort | Saburov, Mansoor |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T16:09:53Z |
| format | Article |
| id | iium-45055 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T16:09:53Z |
| publishDate | 2015 |
| publisher | Thailands National Science & Technology Development Agency |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| spellingShingle | QA Mathematics Saburov, Mansoor Ahmad, Mohd Ali Khameini Quadratic equations over p-adic fields and their applications in statistical mechanics |
| title | 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_short | 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 |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/ http://irep.iium.edu.my/45055/1/Quadratic_Equation_---_SA.pdf |