Mean values of $L$-functions and relative class numbers of cyclotomic fields

Stéphane Louboutin (1)

1 IML - Institut de mathématiques de Luminy

Using formulas for quadratic mean values of L-functions at s = 1, we recover previously known explicit upper bounds on relative class numbers of cyclotomic fields. We also obtain new better bounds.

Mots clés: cyclotomic field; class number; relative class number

Domaines: Théorie des nombres [math.NT]

Stéphane Louboutin. Mean values of $L$-functions and relative class numbers of cyclotomic fields. Publicationes Mathematicae Debrecen, 2011, 78 (3-4), pp.647-658. ⟨10.5486/PMD.2011.4882⟩. ⟨hal-01286334⟩