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Results tagged with algebraic-number-theory
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user 10670
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
2k
views
Greatest common divisor of algebraic integers
I have several questions concerning some properties of algebraic numbers. The first concerns the folowing statement:
Given algebraic integers $\alpha$ and $\beta$ they have a unique greatest common …
- 854
12
votes
Is there an algorithm for determining whether an expression involving nested radicals is rat...
One possible algorithm (I fear that terribly slow) would be to produce all algebraic conjugates of your expression (substituting in every possible way each radical by all it's conjugates) and finding …
- 854