no. 1
Lower bounds for regulators of number fields in terms of their discriminants
Akhtari, Shabnam1 ; Vaaler, Jeffrey D.2
1 Department of Mathematics, University of Oregon, Eugene, Oregon 97403 USA
2 Department of Mathematics, University of Texas, Austin, Texas 78712 USA
Journal de théorie des nombres de Bordeaux, Tome 35 (2023) no. 1, pp. 259-282

We prove inequalities that compare the regulator of a number field with the absolute value of its discriminant. We refine the ideas in Silverman’s work [15] where such general inequalities are first proven. In order to prove our main theorems, we combine these refinements with the authors’ previous results on bounding the product of heights of relative units in a number field extension.

Nous prouvons une inégalité qui compare le régulateur d’un corps de nombres et la valeur absolue de son discriminant. Nous affinons les idées de Silverman [15] où de telles inégalités ont été prouvées pour la première fois. Pour démontrer nos théorèmes principaux, nous combinons ces méthodes avec les bornes pour le produit des hauteurs des unités relatives d’une extension de corps de nombres démontrées dans notre article antérieur.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jtnb.1245
Classification : 11G50, 11R04, 11R27
Keywords: Regulator and discriminant of a number field, Weil height, Arakelov height

Akhtari, Shabnam 1 ; Vaaler, Jeffrey D. 2

1 Department of Mathematics, University of Oregon, Eugene, Oregon 97403 USA
2 Department of Mathematics, University of Texas, Austin, Texas 78712 USA
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Akhtari, Shabnam; Vaaler, Jeffrey D. Lower bounds for regulators of number fields in terms of their discriminants. Journal de théorie des nombres de Bordeaux, Tome 35 (2023) no. 1, pp. 259-282. doi: 10.5802/jtnb.1245

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