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Results tagged with algebraic-number-theory
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user 76440
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
3
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Is the Cassels "$x - \theta$" map algebraic in some sense?
Setup: Let $k$ be a field of characteristic $0$, let $f(x) \in k[x]$ be a monic separable polynomial of degree $n \geq 4$, and let $\theta$ denote the image of $x$ under the map $k[x] \to K_f := k[x]/ …
4
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Convergence in Product Formula for Tamagawa Number
Let $G = \operatorname{SL}_n$, and recall that its Tamagawa number is $\tau(G) = 1$ and is given by the product expansion
$$\tau(G) = \operatorname{Vol}(G(\mathbb{Z})\backslash G(\mathbb{R})) \cdot \p …
6
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From Bhargava to Gauss -- Why does correspondence of cubes and ideal classes imply Gauss cor...
In his seminal 2004 paper "Higher Composition Laws I" in the Annals of Mathematics, (doi:10.4007/annals.2004.159.217), Bhargava proves that for fixed $D \neq 0$, there is a bijective correspondence be …