Conjectures of p-adic L-functions

14.03.2023 13:15 - 14:45

Sheng-Chi Shih (U Vienna)

There are results and conjectures linking important arithmetic properties of number-theoretic objects to special values of their L-functions such as Birch-Swinnerton-Dyer conjecture. One way to attack these conjectures is through the study of p-adic L-functions. In this talk, we introduce, based on examples of ordinary modular forms, conjectures related to p-adic L-functions such as p-adic Birch-Swinnerton-Dyer conjecture, Iwasawa main conjecture, the conjecture of Coates and Perrin-Riou, etc. If time permits, we will report recent results on Iwasawa main conjecture for ordinary modular forms (joint with Jun Wang) and p-adic L-functions for GSp(4) (joint with Adel Betina and Harald Grobner).


H. Grobner, A. Mellit


SR 12, 2. OG, OMP 1