## Number Theory - Siddhi Pathak (Queen's University)

### Wednesday, March 28th, 2018

**Time:** 2:15 p.m. **Place:** Jeffery Hall 319

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

**Title:** On the primitivity of Dirichlet characters.

**Abstract:** ** ** A Dirichlet character modulo q is said to be imprimitive if it is induced from a lower level. A characterization of the primitivity of characters is the separability of the Gauss sum ( Fourier transform of $\chi$ ), i.e., $G_q(n, \bar{chi}) = \chi(n) G_q(1, \bar{ \chi } )$ for all n. In this talk, we discuss a paper of R. Daielda and N. Jones in which they introduce another way of extending primitive Dirichlet characters so that the above separability property holds even for imprimitive characters.