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A connection between uniqueness of the Riemann zeta function and the Riemann hypothesis and beyond

Volume 207 / 2023

Pei-Chu Hu, Bao Qin Li Acta Arithmetica 207 (2023), 183-200 MSC: Primary 11M06; Secondary 30D30. DOI: 10.4064/aa220924-9-1 Published online: 28 February 2023


We establish a connection between the uniqueness of the Riemann zeta function in terms of value distribution and the Riemann hypothesis, which leads to new uniqueness theorems, necessary and sufficient conditions for the Riemann hypothesis, and estimates on asymmetric and symmetric differences of nontrivial zeros of L-functions.


  • Pei-Chu HuDepartment of Mathematics
    Shandong University
    Jinan 250100, Shandong, P.R. China
  • Bao Qin LiDepartment of Mathematics and Statistics
    Florida International University
    Miami, FL 33199, USA

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