Broughan K. Equivalents of the Riemann Hypothesis. Volume 3: Further Steps towards Resolving the Riemann Hypothesis

Cambridge University Press, 2023. — xx, 684 p. — (Encyclopedia of Mathematics and its Applications, 187). — ISBN 978-1-009-38480-3.The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH offers a full presentation of recent results of Nicolas, Rogers–Tao–Dobner, Polymath15, Bagchi, and Matiyasevich. Of particular interest here are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included is the classical Pólya–Jensen equivalence and related developments of Ono et al.
An extensive set of appendices highlights 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 research problems in number theory.
Each of the three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic equivalents to RH. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on the decidability of RH.True PDF