## Number Theory Seminar

### Wednesday, August 1st, 2018

**Time:** 2:30-3:20p.m. **Place:** Jeffery Hall 422

**Speaker:** Siddhi Pathak (Queen's University)

**Title:** Adjoint of the Serre derivative, Poincaré series and special values of shifted Dirichlet series.

**Abstract:** The Serre derivative is a linear differential operator from the space of modular forms of weight k to the space of modular forms of weight k+2. In this talk, we compute the adjoint of the Serre derivative with respect to the Petersson inner product, as done by A. Kumar. Using this as a pretext, we will highlight the connection between the Serre derivative and special values of shifted Dirichlet series via the tool of Poincaré series.