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Numerical
secondary terms in a Cohen–Lenstra conjecture on real
quadratic fields
Codie Lewis and Cassandra Williams
Vol. 12 (2019), No. 2, 221–233
DOI: 10.2140/involve.2019.12.221
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Abstract |
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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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Keywords
Cohen–Lenstra, real quadratic field, secondary term
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Mathematical Subject Classification 2010
Primary: 11R29
Secondary: 11R11, 11Y35
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Milestones
Received: 15 June 2017
Revised: 8 March 2018
Accepted: 11 June 2018
Published: 8 October 2018
Communicated by Yves-François Pétermann
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Authors |
| Codie Lewis | |
| Department of Mathematics Colorado State University Fort Collins, CO United States |
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| Cassandra Williams | |
| Department of Mathematics and
Statistics James Madison University Harrisonburg, VA United States |
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