Back to Departmental Colloquium: Spring 2005
Departmental Colloquium
Date: Tuesday, Feb 8, 2005
Time: 4:15PM
Location: JWB 335
Special Colloquium Tuesday
Heegner Points and Modular Forms
Title |
Heegner Points and Modular Forms |
Abstract |
Modular forms play an increasingly central role in modern number theory. One classical example is the famous j -invariant whose values at Heegner points, i.e., at quadratic irrationalities in the upper half plane, are known as singular moduli and are of particular arithmetic interest. Recently, Zagier realized the generating series of the traces of the singular moduli as a meromorphic modular form of weight 3/2. In this talk, we give an introduction to the subject, discussing this work and related results and provide a generalization to modular functions on Riemann surfaces of arbitrary genus. Furthermore, we realize a certain generating series of arithmetic intersection numbers and Faltings heights of Heegner points as the derivative of Zagier’s Eisenstein series of weight 3/2. |
Number Theory
Algebraic Geometry