Morningside Center of Mathematics
Chinese Academy of Sciences
Morningside Center of Mathematics
Chinese Academy of Sciences
| Title: | The Hasse-Weil zeta function of modular curves(I) |
| Speaker: | William Casselman () |
| Time: | 2015-4-20, 15:30-17:00 |
| Place: | 610 |
| Abstract: | More than 50 years ago, Eichler first proved that the Hasse-Weil zeta function of a modular curve was the same as one of Hecke's. New proofs of this were given by Shimura, Ihara, and then Langlands.Langlands' methods have since been extended to include many other modular varieties, but his original paper was necessarily complicated, since it proved quite a bit more than the basic result. A full and elementary account of it does not apparently exist. That is what I hope to present in four lectures. I'll also comment on later generalizations. Outline: a. Introduction b. The basic equation c. Counting elliptic curves over finite fields d. Applying the Trace Formula |
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