This is a collection of some introductory resources for the area of “arithmetic statistics”:
- Arithmetic Statistics: Elliptic Curves and Other Things, by Barry Mazur.
- Finding meaning in error terms, by Barry Mazur.
- Video lectures from an MSRI workshop on Arithmetic Statistics (2011).
- Notes from the Arizona Winter School on Arithmetic Statistics (2014).
- Asymptotics for Number Fields and Class Groups, by Melanie Matchett Wood.
- SMS summer school on Counting Arithmetic objects.
- Schedule of talks with links to the notes/slides for the talks.
- Resources for a course on Arithmetic statistics and Bhargavology taught by Rob Harron.
Prime numbers:
- Prime Number Races, by Andrew Granville and Greg Martin.
- Harald Cramer and the distribution of prime numbers, by Andrew Granville.
- An Amazing Prime Heuristic (unfinished), by Chris Caldwell.
- Unexpected biases in the distribution of consecutive primes, by Robert Lemke Oliver and Kannan Soundararajan.
- The quest for narrow admissible tuples, by Andrew Sutherland.
Number Fields:
- The density of discriminants of quartic rings and fields, by Manjul Bhargava.
Class Groups:
- The Cohen-Lenstra Heuristic: Methodology and Results, by Johannes Lengler (and Lengler’s thesis).
- Asymptotics for Number Fields and Class Groups, by Melanie Matchett Wood.
Quadratic Forms:
- Composing quadratic forms: Gauss, Dirichlet, and Bhargava, by Andrew Granville.
Elliptic Curves:
- Average ranks of elliptic curves: tension between data and conjecture, Baur Bektemirov, Barry Mazur, William Stein, Mark Watkins.
- A heuristic for boundedness of ranks of elliptic curves, by Jennifer Park, Bjorn Poonen, John Voight, Melanie Matchett Wood.
- Heuristics for the arithmetic of elliptic curves, by Bjorn Poonen.