On elliptic curves and random matrix theory

Watkins, Mark

Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 3, pp. 829-845.

Rubinstein a accumulé une masse de données concernant les tordues quadratiques paires d’une courbe elliptique fixée, et comparé les résultats aux prédictions venues du modèle des matrices aléatoires. Nous utilisons la méthode des points de Heegner pour obtenir des données comparables (en nombre plus faible) pour les tordues impaires. Nous constatons de nouveau qu’au moins une des principales prédictions de la théorie des matrices aléatoires est confortée par les données.

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.

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