Yau Mathematical Sciences Center, Tsinghua University and Institute for Advanced Study
Eisenstein congruences and special values of L functions.
Mazur (1979) noticed that in some cases an Eisenstein congruence could imply a congruence between special values of L functions. One can then obtain some results toward conjectures like the Bloch-Kato conjecture. In a recent joint work with Jun Wang, we obtain such results for certain modular forms twisted by quadratic characters of real quadratic fields.
We will report on these results, and propose a research direction in the case of imaginary quadratic fields.