Displaying similar documents to “Bounds for the degrees of CM-fields of class number one”

On the number of rational points of Jacobians over finite fields

Philippe Lebacque, Alexey Zykin (2015)

Acta Arithmetica

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We prove lower and upper bounds for the class numbers of algebraic curves defined over finite fields. These bounds turn out to be better than most of the previously known bounds obtained using combinatorics. The methods used in the proof are essentially those from the explicit asymptotic theory of global fields. We thus provide a concrete application of effective results from the asymptotic theory of global fields and their zeta functions.

Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems

Stéphane R. Louboutin (2007)

Colloquium Mathematicae

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We give a simple proof of the Siegel-Tatuzawa theorem according to which the residues at s = 1 of the Dedekind zeta functions of quadratic number fields are effectively not too small, with at most one exceptional quadratic field. We then give a simple proof of the Brauer-Siegel theorem for normal number fields which gives the asymptotics for the logarithm of the product of the class number and the regulator of number fields.