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Results tagged with algebraic-number-theory
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user 1306
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
1
vote
How do I find abelian cubic extension over $\mathbb{Q}$ with class number more than 1?
The earliest result I know which leads to many examples is that of Uchida:
Uchida, K.:
Class numbers of cubic cyclic fields.
J. Math. Soc. Japan 26(3): 447-453 (July, 1974)
See also Washington, L. …
- 16.9k
56
votes
Accepted
Minimal polynomial of cos(π/n)
The minimal polynomial of $\cos(2\pi/n)$ (by William Watkins and Joel Zeitlin, The American Mathematical Monthly
Vol. 100, No. 5 (May, 1993), pp. 471-474) has full clarity on this matter (just take th …
- 16.9k
13
votes
linear independence of $\sin(k \pi / m)$
We have
$$\sin\frac{\pi}{9}+\sin\frac{2\pi}9-\sin\frac{4\pi}9=\sin\frac{2\pi}{18}+\sin\frac{4\pi}{18}-\sin\frac{8\pi}{18}=\sin\frac{2\pi}{18}-\sin\frac{8\pi}{18}+\sin\frac{14\pi}{18},$$
and the latte …
- 16.9k