Keith Ball – Rational approximations to ζ

Enrico Bombieri – Pseudo-Laplacians: a special case

Alain Connes – The Riemann-Roch strategy

Brian Conrey – *L*-functions and random matrix theory

Paul Garrett – Self-adjoint operators on automorphic forms

Nicholas M. Katz – RH in characteristic *p*: the importance of family values

S. J. Patterson – The context of Riemann’s paper on the distribution of prime numbers

Maksym Radziwill – Some analogies

Peter Sarnak – Commentary and comparisons of some approaches to GRH

Fernando Rodriguez Villegas – Hypergeometric motives

Wei Zhang – Positivity of *L*-functions and “completion of the square”