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Results tagged with algebraic-number-theory
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user 60519
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
4
votes
Weber's class number problem and real quadratic fields of class number one
Let $K$ be any subextension of $F_n$. Then the natural map of class groups $\text{Cl}(K) \rightarrow \text{Cl}(F_n)$ is an injection. Indeed, you can see it in terms of unramified abelian extension vi …
- 1,109
19
votes
Elementary congruences and L-functions
I answer only for the $3$-part of your question (I have to think more for the $2$-part).
Let $N$ be a prime $\equiv 1 \text{ (mod } 3\text{)}$. Let $\text{log} : (\mathbf{Z}/N\mathbf{Z})^{\times} \ …
- 1,109