5 papers
Split-CM points and central values of Hecke L-series
Kimberly Hopkins
Split-CM points are points of the moduli space h_2/Sp_4(Z) corresponding to products of elliptic curves with the same complex multiplication. We prove that the number…
Higher Weight Heegner Points
Kimberly Hopkins
In this paper we formulate a conjecture which partially generalizes the Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N) satisfying certain conditions, w…
Lower bounds for the principal genus of definite binary quadratic forms
Kimberly Hopkins, Jeffrey Stopple
We apply Tatuzawa's version of Siegel's theorem to derive two lower bounds on the size of the principal genus of positive definite binary quadratic forms.
Bounds on discriminants with one class per genus
Kimberly Hopkins
We assume a condition on the zeros of Dirichlet L-functions related to the GUE distribution to show there are no discriminants greater than d_{66}\approx 1.9 x 10^{130} with one cl…
Quadratic reciprocity in a finite group
William Duke, Kimberly Spears
In this article we define a quadratic symbol for a finite group and prove a law of reciprocity for its value.