Cubic equations over p-adic field and their applications /
In this thesis, we did a research on cubic equations over p-adic field Qp where p is a prime number. In the first part, we studied the general cubic equations over Qp where p >3. We described the location of roots of the general cubic equation without knowing their exact values. Furthermore, we g...
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| Main Author: | |
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| Format: | Thesis |
| Language: | English |
| Published: |
Kuantan, Pahang :
Kulliyyah of Science, International Islamic University Malaysia,
2016
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| Subjects: | |
| Online Access: | Click here to view 1st 24 pages of the thesis. Members can view fulltext at the specified PCs in the library. |
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| Summary: | In this thesis, we did a research on cubic equations over p-adic field Qp where p is a prime number. In the first part, we studied the general cubic equations over Qp where p >3. We described the location of roots of the general cubic equation without knowing their exact values. Furthermore, we gave the solvability criterion and the number of roots of the general cubic equation over Zp; Zp \ Zp; Qp nZp and Qp. In the second part, we discussed the depressed cubic equations over p-adic field. We provided the exact location of roots of the depressed cubic equation over p-adic field for p > 3. For p = 3, we provided the solvability criterion and the number of roots of the depressed cubic equation over Z3; Z3 \ Z3; Q3 \ Z3 and Q3. While, for p D 2, we provided the solvability criterion of the depressed cubic equation over Z2; Z2 \ Z2; Q2 \ Z2 and Q2. In the last part, we presented the application of the cubic equations in the p-adic Potts model. We described all translation invariant p-adic Gibbs measures for the Potts model on Cayley tree of order three by giving all possible forms of boundary functions. We showed that the boundary functions can be described in terms of roots of some general cubic equations over some domains of p-adic field. |
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| Physical Description: | x, 162 leaves : ill. ; 30cm. |
| Bibliography: | Includes bibliographical references (leaves 157-160). |