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2019 Numerical secondary terms in a Cohen–Lenstra conjecture on real quadratic fields
Codie Lewis, Cassandra Williams
Involve 12(2): 221-233 (2019). DOI: 10.2140/involve.2019.12.221

Abstract

In 1984, Cohen and Lenstra 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.

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Codie Lewis. Cassandra Williams. "Numerical secondary terms in a Cohen–Lenstra conjecture on real quadratic fields." Involve 12 (2) 221 - 233, 2019. https://doi.org/10.2140/involve.2019.12.221

Information

Received: 15 June 2017; Revised: 8 March 2018; Accepted: 11 June 2018; Published: 2019
First available in Project Euclid: 25 October 2018

zbMATH: 06980499
MathSciNet: MR3864215
Digital Object Identifier: 10.2140/involve.2019.12.221

Subjects:
Primary: 11R29
Secondary: 11R11 , 11Y35

Keywords: Cohen–Lenstra , real quadratic field , secondary term

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2019
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