On the Applications of Cyclotomic Fields in Introductory Number Theory
| Autor: | Kabalan Gaspard |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
Dirichlet Root of unity Mathematics::Number Theory Real Units Primary Units Plant Science Dirichlet distribution Prime (order theory) symbols.namesake Number Theory Kummer Fermat's Last Theorem FOS: Mathematics Physical Sciences and Mathematics Number Theory (math.NT) Mathematics Pell's Equation Cyclotomic Fields Mathematics - Number Theory Forestry Number theory symbols Pell's equation Agronomy and Crop Science |
| Zdroj: | Gaspard, Kabalan. (2013). On the Applications of Cyclotomic Fields in Introductory Number Theory. Berkeley Scientific Journal, 17(1). Retrieved from: http://www.escholarship.org/uc/item/49c0561x |
| Popis: | In this essay, we see how prime cyclotomic fields (cyclotomic fields obtained by adjoining a primitive p-th root of unity to Q, where p is an odd prime) can lead to elegant proofs of number theoretical concepts. We namely develop the notion of primary units in a cyclotomic field, demonstrate their equivalence to real units in this case, and show how this leads to a proof of a special case of Fermat's Last Theorem. We finally modernize Dirichlet's solution to Pell's Equation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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