Equivalents of the Riemann Hypothesis: Volume 3, Further Steps towards Resolving the Riemann Hypothesis

Kevin Broughan is an emeritus professor at the University of Waikato, New Zealand. He cofounded and is a fellow of the New Zealand Mathematical Society and the School of Computing and Mathematical Sciences. Broughan previously authored Volumes 1 and 2 of 'Equivalents of the Riemann Hypothesis' (Cambridge 2017) and 'Bounded Gaps Between Primes' (Cambridge 2021). He also wrote the software package that is part of Dorian Goldfeld's book 'Automrphic Forms and L-Functions for the Group GL(n,R)' (Cambridge 2006).

1. Nicolas' π(x) < li(θ(x)) equivalence; 2. Nicolas' number of divisors function equivalence; 3. An aspect of the zeta function zero gap estimates; 4. The Rogers–Tao equivalence; 5. The Dirichlet series of Dobner; 6. An upper bound for the deBruijn–Newman constant; 7. The Pólya–Jensen equivalence; 8. Ono et al. and Jensen polynomials; 9. Gonek–Bagchi universality and Bagchi's equivalence; 10. A selection of undecidable propositions; 11. Equivalences and decidability for Riemann's zeta; A. Imports for Gonek's theorems; B. Imports for Nicolas' theorems; C. Hyperbolic polynomials; D. Absolute continuity; E. Montel and Hurwitz's theorems; F. Markov and Gronwall's inequalities; G. Characterizing Riemann's zeta function; H. Bohr's theorem; I. Zeta and L-functions; J. de Reyna's expansion for the Hardy contour; K. Stirling's approximation for the gamma function; L. Propositional calculus $/mathscr{P}_0$; M. First order predicate calculus $/mathscr{P}_1$; N. Recursive functions; O. Ordinal numbers and analysis; References; Index