摘要翻译:
在以前的工作中,第一作者提出了一种计算Hilbert模形式的算法。本文将此推广到所有偶数度的全实数域和非平凡类群。利用$\q(\sqrt{10})$和$\q(\sqrt{85})$及其Hilbert类域上的算法,给出了完全实域的猜想Eichler-Shimura构造的一些新实例,特别是找到了具有处处良好约简的模阿贝尔变体的新实例。
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英文标题:
《Computing Hilbert modular forms over fields with nontrivial class group》
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作者:
Lassina Dembele and Steve Donnelly
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over $\Q(\sqrt{10})$ and $\Q(\sqrt{85})$ and their Hilbert class fields, we present some new instances of the conjectural Eichler-Shimura construction for totally real fields, and in particular find new examples of modular abelian varieties with everywhere good reduction.
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PDF链接:
https://arxiv.org/pdf/0711.3863