HauptmenΓΌ
  • Autor
    • Yang, Daodao
  • TitelExtreme values of derivatives of the Riemann zeta function
  • Datei
  • DOI10.1112/mtk.12130
  • Erschienen inMathematika
  • Band68
  • Erscheinungsjahr2022
  • Heft2
  • Seiten486-510
  • LicenceCC BY-NC-ND 4.0
  • ISSN2041-7942
  • ZugriffsrechteCC-BY
  • Download Statistik19
  • Peer ReviewJa
  • AbstractIt is proved that if 𝑇 is sufficiently large, then uniformly for all positive integers 𝓁 β©½ (log 𝑇)βˆ•(log2 𝑇), we have \( \max_{𝑇⩽𝑑⩽2𝑇} 𝜁^{(l)} 1 + 𝑖𝑑| β©Ύ 𝑒^𝛾 β‹… l^l β‹… (l + 1)^{βˆ’(l+1)} β‹… ( log_2𝑇 βˆ’log_3𝑇 +𝑂(1)^{l+1}\) , where 𝛾 is the Euler constant. We also establish lower bounds for maximum of \(|𝜁^{(l)}(𝜎 + 𝑖𝑑)|\) when 𝓁 ∈ β„• and 𝜎 ∈ [1βˆ•2, 1) are fixed. MSC (202 0 ) 11M06 (primary)