Upper bounds on relative class numbers of cyclotomic fields

Stéphane Louboutin (1)

1 I2M - Institut de Mathématiques de Marseille

We explain how one can use the explicit formulas for the mean square values of L-functions which we established elsewhere to obtain explcit upper bounds on relative class numbers of cyclotomic number fields. As an example, we show that the relative class numbers of the cyclotomic fields of conductor 4p, p ≥ 3 a prime, are less than or equal to 8√p(p/16)(p−1)/2.

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

Domaines: Théorie des nombres [math.NT]

Stéphane Louboutin. Upper bounds on relative class numbers of cyclotomic fields. Mathematica Slovaca, 2014, 64 (1), pp.21-26. ⟨10.2478/s12175-013-0183-5⟩. ⟨hal-01286421⟩