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Two upper bounds for the Erdős-Hooley Delta-function

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Abstract

For integer n ⩾ 1 and real u, let Δ(n, u):= ∣{d: d ∣ n, eu < d ⩽ eu+1}∣. The Erdős-Hooley Delta-function is then defined by Δ(n):=maxu∈ℝ Δ(n, u). We improve the current upper bounds for the average and normal orders of this arithmetic function.

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Authors and Affiliations

  1. Institut de Mathématiques, Université Paris Cité, Sorbonne Université, CNRS, Paris, F-75013, France

    Régis de la Bretèche

  2. Institut Élie Cartan, Université de Lorraine, Vandœuvre-lès-Nancy, BP 70239, France

    Gérald Tenenbaum

Authors
  1. Régis de la Bretèche
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  2. Gérald Tenenbaum
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Correspondence to Gérald Tenenbaum.

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On the 50th anniversary of Chen’s theorem

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de la Bretèche, R., Tenenbaum, G. Two upper bounds for the Erdős-Hooley Delta-function. Sci. China Math. 66, 2683–2692 (2023). https://doi.org/10.1007/s11425-022-2193-8

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  • DOI: https://doi.org/10.1007/s11425-022-2193-8

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