平特五不中

Title:

听Congruences between automorphic forms

听

Abstract:

The theory of congruences between automorphic forms traces back to Ramanujan, who observed various congruence properties between coefficients of generating functions related to the partition function. Since then, the subject has evolved to become a central piece of contemporary number theory, lying at the heart of spectacular achievements such as the proof of Fermat's Last Theorem and the Sato-Tate conjecture. In my talk I will explain how the modern theory gives satisfactory explanations of some concrete phenomena for modular forms (the GL_2 case), and discuss recent progress concerning automorphic forms for higher rank groups.