Numerical secondary terms in a Cohen-Lenstra conjecture on real quadratic fields. (English) Zbl 1458.11158

Lewis, Codie; Williams, Cassandra

Involve 12, No. 2, 221-233 (2019).

Summary: In [Lect. Notes Math. 1068, 33–62 (1984; Zbl 0558.12002)], H. Cohen and H. W. Lenstra jun. made a number of conjectures regarding the class groups of quadratic fields. In particular, they predicted the proportion of real quadratic fields with class number divisible by an odd prime. We numerically investigate the difference between reality and these predictions. Using 4 million data points, we perform a curve fitting of the difference with a monomial term and demonstrate that there is reason to believe the term can be effectively approximated within the scope of our data set for odd primes less than 30. We use cross-validation to show that including our monomial term as a secondary term to the original conjecture reduces the overall error.

MSC:

11R29	Class numbers, class groups, discriminants
11R11	Quadratic extensions
11Y35	Analytic computations

Keywords:

Cohen-Lenstra; real quadratic field; secondary term

Citations:

Zbl 0558.12002

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