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, Bagchi, and Matiyasevich. Of particular interest here are derivations showing 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 results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. 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.

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.

The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.