Displaying similar documents to “Computer-aided serendipity”

Why is the class number of ℚ ( 11 3 ) even?

F. Lemmermeyer (2013)

Mathematica Bohemica

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In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.

L.J. Mordell

H. Davenport (1964)

Acta Arithmetica

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On elliptic curves and random matrix theory

Mark Watkins (2008)

Journal de Théorie des Nombres de Bordeaux

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Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.