Abstract: For a regular algebraic cuspidal automorphic representation of $\mathrm{G}\mathrm{L}(n)$, one obtains natural rational structures arising from Betti cohomology and from the Whittaker model. Understanding the relation between these structures is fundamental to the study of special values of automorphic $L$-functions and their arithmetic properties. In this talk, I will explain the construction of these rational structures and discuss a recent comparison result relating the Betti–Whittaker periods attached to a regular automorphic representation and to its dual representation. I will also describe some consequences and motivations coming from the theory of automorphic $L$-functions and period relation.

 

Organizer: Shih-Yu Chen (NTHU)