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15
387
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Decomposition field of $x^n - 1$ over $Z_p$

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#field-theory #extension-field #roots-of-unity
128
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Expressing $\zeta^k+\zeta^{-k}$ as a polynomial in $\zeta+\zeta^{-1}$.

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#algebraic-number-theory #roots-of-unity #cyclotomic-fields #chebyshev-polynomials
116
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holomorphic functions, roots of unity and harmonic numbers

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#complex-analysis #holomorphic-functions #roots-of-unity #harmonic-numbers
54
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Notation and interpretation of Polynomials in $\mathbb{F}_{p}[x]$

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#group-theory #polynomials #irreducible-polynomials #roots-of-unity #cyclotomic-polynomials
42
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Complex Endomorphism $f$ with orthogonal Eigenspaces implies that $f$ is unitary

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#eigenvalues-eigenvectors #orthogonality #roots-of-unity
437
Views

Galois theory: Gauss-Wantzel theorem, proof explanation

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#galois-theory #proof-explanation #minimal-polynomials #roots-of-unity #geometric-construction
76
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Showing the lemma $\operatorname{ord}_p(1+ζ_p)=0$ if $p>2$

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#abstract-algebra #field-theory #prime-numbers #p-adic-number-theory #roots-of-unity
83
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Proving $ord_p(ζ_p-1)=1/(p-1)$

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#abstract-algebra #prime-numbers #extension-field #p-adic-number-theory #roots-of-unity
38
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Roots of sparse "quadratic-like" polynomial.

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#polynomials #factoring #roots-of-unity
100
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Relation between the numbers of units, square roots of unity and divisors for the rings $\mathbb{Z}/n\mathbb{Z}$

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#elementary-number-theory #roots-of-unity
205
Views

Are the prime cyclotomic polynomials irreducible over any field where they're not obviously reducible ?

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#galois-theory #irreducible-polynomials #roots-of-unity #galois-extensions
149
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Compute $\sum\frac1{2-A_k}$ for $(A_k)$ the $n$th roots of unity

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#polynomials #complex-numbers #summation #roots #roots-of-unity
37
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5-adic order of $\zeta-f(\overline 2)\zeta^2+f(\overline 2)\zeta^3+\zeta^4$

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#abstract-algebra #field-theory #prime-numbers #roots-of-unity
199
Views

cardinality of Galois group in $\mathbb{Q}$($\zeta_n$)

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#abstract-algebra #number-theory #galois-theory #roots-of-unity #galois-extensions
134
Views

"Converse" to the theorem "sum of roots of unity equal 0"

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#roots-of-unity

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