Note, that for n ≡ 2 mod 4 the relative cyclotomic units are trivial!
Note that the union of all bases over all n extends to a universal basis
The rank (number of elements in basis) is 0
Note, that for n ≡ 2 mod 4 the relative cyclotomic units are trivial!
v(14,1) |
v(14,3) |
v(14,5) |
v(14,9) |
v(14,11) |
v(14,13) |
Note, that for n ≡ 2 mod 4 the relative cyclotomic units are trivial!
Note that equality is modulo multiplication by an n^{th} unit root and modulo d^{th} cyclotomic units where d is a proper divisor of n.
1: v(14,1) = 1Note, that for n ≡ 2 mod 4 the relative cyclotomic units are trivial!
Compare with Algorithm 1.2 and 2.2
1: v(14,1) - method Z-2 (Case IV - A12)
3: v(14,3) - method Z-2 (Case IV - A12)
5: v(14,5) - method Z-2 (Case IV - A12)
9: v(14,9) - method Z-2 (Case IV - A12)
11: v(14,11) - method Z-2 (Case IV - A12)
13: v(14,13) - method Z-2 (Case IV - A12)
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© by: Marc Conrad, 2016. If you want me
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The material on this page is presented "as is". There is no warranty implied by presenting this stuff. Feel free to use and modify the material for your own teaching. When doing so please link to this web site (http://perisic.com/cyclotomic). In acadmic publications cite this page as: Conrad, Marc (2016) Cyclotomic Units - Relations and Computations (online), available at: http://perisic.com/cyclotomic. The webspace for this project is kindly provided by the Perisic Guesthouse (www.perisic.com). |