EXPLICIT UPPER BOUNDS FOR THE RESIDUES AT s = 1 OF THE DEDEKIND ZETA FUNCTIONS OF SOME TOTALLY REAL NUMBER FIELDS
نویسنده
چکیده
— We give an explicit upper bound for the residue at s = 1 of the Dedekind zeta function of a totally real number field K for which ζK(s)/ζ(s) is entire. Notice that this is conjecturally always the case, and that it holds true if K/Q is normal or if K is cubic. Résumé (Bornes supérieures explicites pour les résidus en s = 1 des fonctions zêta de Dedekind de corps de nombres totalement réels) Nous donnons une borne supérieure explicite pour le résidu en s = 1 de la fonction zêta de Dedekind d’un corps de nombres K totalement réel pour lequel ζK(s)/ζ(s) est entière. On remarque que c’est conjecturalement toujours le cas, et que c’est vrai si K/Q est normale ou si K est cubique.
منابع مشابه
On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
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 ...
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