Displaying similar documents to “Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions : a survey of recent results”

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.

On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes

Stéphane Louboutin (2005)

Journal de Théorie des Nombres de Bordeaux

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Lately, explicit upper bounds on | L ( 1 , χ ) | (for primitive Dirichlet characters χ ) taking into account the behaviors of χ on a given finite set of primes have been obtained. This yields explicit upper bounds on residues of Dedekind zeta functions of abelian number fields taking into account the behavior of small primes, and it as been explained how such bounds yield improvements on lower bounds of relative class numbers of CM-fields whose maximal totally real subfields are abelian. We present...