Real zeros of Dedekind zeta functions

Stéphane Louboutin (1)

1 I2M - Institut de Mathématiques de Marseille

Building on Stechkin and Kadiri's ideas we derive an explicit zero-free region of the real axis for Dedekind zeta functions of number fields. We then explain how this new region enables us to improve upon the previously known explicit lower bounds for class numbers of number fields and relative class numbers of CM-fields.

Mots clés: Dedekind zeta function; real zero; Siegel zero

Domaines: Théorie des nombres [math.NT]

Stéphane Louboutin. Real zeros of Dedekind zeta functions. International Journal of Number Theory, 2015, 11 (03), pp.843-848. ⟨10.1142/S1793042115500463⟩. ⟨hal-01287999⟩