Tag Archives: Stark

Real quadratic fields and finite quantum dilogarithms I

Posted on September 22, 2026 by Persiflage

Danylo Radchenko and Campbell Wheeler have posted an extraordinary new paper in which they prove that Stark units for real quadratic fields are algebraic numbers. (Not yet a Shimura reciprocity law that shows these generate abelian extensions but hey, this … Continue reading →

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The Artin conjecture is rubbish

Posted on September 10, 2014 by Persiflage

Let \(\rho: G_{\mathbf{Q}} \rightarrow \mathrm{GL}_N(\mathbf{C})\) be a continuous irreducible representation. Artin conjectured that the L-function \(L(\rho,s)\) is analytically continues to an entire function on \(\mathbf{C}\) (except for the trivial representation where the is a simple pole at one) and satisfies … Continue reading →

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K_2(O_F) for number fields F

Posted on September 4, 2014 by Persiflage

Belabas and Gangl have a nice paper ( Generators and relations for \(K_2({\mathcal{O}}_F)\), which can be found here) where they compute \(K_2({\mathcal{O}}_E)\) for a large number of quadratic fields \(E\). There main result is a method for proving upper bounds … Continue reading →

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