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.