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Results tagged with algebraic-number-theory
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user 129192
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
16
votes
2
answers
1k
views
Is it decidable whether two real algebraic irrationals generate the same extension of the ra...
For an algebraic number $\alpha$, let $f_\alpha$ denote its minimal polynomial. We can symbolically represent an algebraic number $\alpha$ by the tuple
$$
(f_\alpha, x, y, r) \in \mathbb{Q}[x] \times …
- 1,087
5
votes
0
answers
180
views
Is there an effective way to compute the square root of an algebraic number?
For an algebraic number $\alpha$, let $f_\alpha$ denote its minimal polynomial. We can symbolically represent an algebraic number $\alpha$ by the tuple
$$
(f_\alpha, x, y, r) \in \mathbb{Q}[x] \times …
- 1,087