Resumen de Effective nonvanishing of canonical Hecke L-functions

George Boxer, Peter Diao

• Motivated by work of Gross, Rohrlich, and more recently Kim, Masri, and Yang, we investigate the nonvanishing of central values of -functions of ``canonical'' weight Hecke characters for , where is prime. Using the work of Rodriguez-Villegas and Zagier, we show that there are nonvanishing central values provided that and . Moreover, we show that the number of such satisfies