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  3. Equivalents of the Riemann Hypothesis
  • Cited by 2
      • Volume 3: Further Steps towards Resolving the Riemann Hypothesis
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    • Publisher:
      Cambridge University Press
      Publication date:
      October 2023
      October 2023
      ISBN:
      9781009384780
      9781009384803
      DOI:
      https://doi.org/10.1017/9781009384780
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.27kg, 706 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Logic, Categories and Sets, Number Theory
      Series:
      Encyclopedia of Mathematics and its Applications (187)
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    Subjects:
    Mathematics (general), Mathematics, Logic, Categories and Sets, Number Theory
    Series:
    Encyclopedia of Mathematics and its Applications (187)
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    Book description

    The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers–Tao–Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included are classical Pólya–Jensen equivalence and related developments of Ono et al. Extensive appendices highlight key background results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. It is ideal for mathematicians wishing to update their knowledge, logicians, and graduate students seeking accessible number theory research problems. The three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic RH equivalents. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on RH decidability.

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