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Non-vanishing of Dirichlet series without Euler products

Abstract : We give a new proof that the Riemann zeta function is nonzero in the half-plane {s ∈ C : σ > 1}. A novel feature of this proof is that it makes no use of the Euler product for ζ(s).
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https://hal.archives-ouvertes.fr/hal-01671237
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Submitted on : Friday, December 22, 2017 - 10:03:28 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

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William D. Banks. Non-vanishing of Dirichlet series without Euler products. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2018, Volume 40 - 2017, pp.31 - 42. ⟨10.46298/hrj.2018.4027⟩. ⟨hal-01671237⟩

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