Galois groups for one class of equations (Q2891020)
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scientific article; zbMATH DE number 6045614
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Galois groups for one class of equations |
scientific article; zbMATH DE number 6045614 |
Statements
12 June 2012
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Euler function
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Chebyshev polynomials
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maximal real subfield
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cyclotomic field
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0.90984464
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0.9052992
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0.90119976
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0.89905316
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Galois groups for one class of equations (English)
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Let \(n\) be a natural number, then \(L_n=\mathbb Q(\mathrm{cos}\frac{\pi}{n})\) is the maximal real subfield of the cyclotomic field \(\mathbb Q(\zeta_{2n})\) and \(L_n/\mathbb Q\) is abelian of degree \(\varphi(2n)/2\). In the paper under review the authors give a recursive formula for the minimal polynomial \(p_n(x)\) of \(\mathrm{cos}\frac{\pi}{n}\) and an explicit description of the Galois group \(G(L_n/\mathbb Q)\).
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