Celebrating 150+ years of the Riemann Hypothesis

Articles (as my research is on the connections between RH and random matrix theory, the list below is a bit biased!)

• English translation of Riemann's paper: standard advice to students / young scholars: read the experts! Try to find in the paper where Riemann mentions his hypothesis -- it's probably the best little aside ever. A scan of the original paper is available here.
• Hayes: The Spectrum of Riemannium: a light description of the connection between random matrix theory and number theory (there are a few minor errors in the presentation, basically to simplify the story). This is a quick read, and gives some of the history.
• Conrey: survey article on the Riemann Hypothesis
• Conrey: L-functions and Random Matrix Theory: This is a high level description of the similarities between number theory and random matrix theory.
• Goldfeld: elementary proof of the prime number theorem
• In my book An Invitation to Modern Number Theory (with Ramin Takloo-Bighash, Princeton University Press), the last part of the book deals with the connections between number theory and random matrix theory. In particular, chapter15 is a nice introduction to the subject.
• Odlyzko: Distribution of spacings between zeros of the zeta function: One of the classics in the field of the phenomenal agreement between the zeros of the Riemann zeta function and the eigenvalues of matrices. See also the 10^22nd zero of the Riemann zeta function, or more generally,Andrew Odlyzko's homepage.
• Diaconis: patterns in eigenvalues
• Keating and Snaith: Random matrix theory and the zeta function
• Tracy and Widom: Introduction to random matrices
• Classic papers:
  • Four papers by Wigner: bordered matrices I        bordered matrices II        roots certain matrices        RMT in physics
  • Four papers by Dyson:  energy levels I                 energy levels II                energy levels III                threefold way

Links to various websites about RH

• AIM's homepage for RH celebrations (including a list of talks worldwide)
• Resources from a graduate workshop on Zeta functions, L-functions and their applications. This is a reference page I made for a conference I attended in Utah in summer '09. The purpose was to introduce graduate students to problems in L-functions and random matrix theory. There are links to many papers there, as well as the slides of many of the talks and my notes from the conference.
• Wikipedia's page on RH

Some talks I've given on the connections between L-functions and random matrix theory