UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Heegner points and the class number of imaginary quadratic fields Verones, Deanna Lynn


Gauss' class number problem is that of finding an upper bound for |D| with given class number h(D) where D is a negative fundamental discriminant. A theorem of Goldfeld reduces the class number problem to finding an elliptic curve defined over Q with rank r > 3 which satisfies the Birch and Swinnerton-Dyer conjecture. A theorem of Gross and Zagier gives a method of predicting when a Heegner point yields rational point of infinite order on an elliptic curve. In some cases their theorem allows us to say for certain whether the derivative of the L-series of an elliptic curve vanishes. Applying their theorem to a particular elliptic curve with rank r = 3, Gross and Zagier were able to show that their curve satisfied the Birch and Swinnerton-Dyer conjecture, thus solving the class number problem. This thesis examines closely the theory of Heegner points including computational results varifying the Gross-Zagier theorem.

Item Media

Item Citations and Data


For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.