A Spectrum Through the Primes: A Concrete Tour of the Spectral and Quantum Approaches (Paperback) (ISBN-13: 9798996732531)

The zeros of the zeta function look like the spectrum of something. What?

A Spectrum Through the Primes pursues the deepest dream in number theory - that the Riemann zeros are the eigenvalues of an undiscovered operator - and refuses to flinch from where it leads. The random-matrix statistics the zeros obey, the Hilbert-Pólya program, the Berry-Keating model, the primon gas, the parity hidden in the Möbius function, and the honest, instructive ways each attempt to build the operator fails: all of it worked concretely, with metaphor kept distinct from mechanism.

Like the rest of the trilogy, it walks up to the same three walls rather than pretending to cross them - and its claims are backed by deterministic Python you can run yourself. A closing chapter rolls the whole picture past the circle onto the lemniscate and the Gaussian integers, and finds the walls standing exactly where it left them. A full set of exercises, with complete worked solutions, is included.

The second book in the Primes Trilogy. It assumes the wheel of Book One but restates what it needs along the way.