Simple zeros of Dedekind zeta functions

Abstract : Using Stechkin's lemma we derive explicit regions of the half complex plane R (s) <= 1 in which the Dedekind zeta function of a number field K has at most one complex zero, this zero being real if it exists. These regions are Stark-like regions, i.e. given by all s = beta + i gamma with beta >= 1 - c = logd(K) and vertical bar gamma vertical bar <= d/logd(K) for some absolute positive constants c and d. These regions are larger and our proof is simpler than recently published such regions and proofs.
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https://hal.archives-ouvertes.fr/hal-01581096
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Submitted on : Monday, September 4, 2017 - 11:49:23 AM
Last modification on : Monday, March 4, 2019 - 2:04:22 PM

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Stéphane R. Louboutin. Simple zeros of Dedekind zeta functions. Functiones et Approximatio Commentarii Mathematici, Poznań : Wydawnictwo Naukowe Uniwersytet im. Adama Mickiewicza, 2017, 56 (1), pp.109 - 116. ⟨10.7169/facm/1598⟩. ⟨hal-01581096⟩

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