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Zeros of Dedekind zeta functions under GRH

Authors: Loïc Grenié and Giuseppe Molteni
Journal: Math. Comp. 85 (2016), 1503-1522
MSC (2010): Primary 11R42
Published electronically: October 9, 2015
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Abstract: Assuming GRH, we prove an explicit upper bound for the number of zeros of a Dedekind zeta function having imaginary part in $ [T-a,T+a]$. We also prove a bound for the multiplicity of the zeros.

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Loïc Grenié
Affiliation: Dipartimento di Ingegneria Gestionale, dell’Informazione e della Produzione, Università di Bergamo, viale Marconi 5, 24044 Dalmine (BG) Italy

Giuseppe Molteni
Affiliation: Dipartimento di Matematica, Università di Milano, via Saldini 50, 20133 Milano, Italy

Received by editor(s): July 4, 2014
Received by editor(s) in revised form: October 18, 2014, and November 7, 2014
Published electronically: October 9, 2015
Article copyright: © Copyright 2015 American Mathematical Society