## Number Theory Seminar

### Wednesday, August 22nd, 2018

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

**Speaker:** Anup Dixit (Queen's University)

**Title:** ON THE UNIVERSALITY OF CERTAIN L-FUNCTIONS.

**Abstract:** In 1975, S. Voronin proved a fascinating result on Riemann zeta-function, which states that every non-vanishing holomorphic function on a compact set in the critical strip $1/2 \Re(s) 1$ is well approximated by vertical shifts of the zeta function, infinitely often. This is called the universality property of the Riemann zeta-function. This property can be shown for many familiar L-functions, for instance all L-functions in the Selberg class are known to be universal. Moreover, functions such as the Hurwitz zeta-function or Lerch zeta-function, which are not elements in the Selberg class also satisfy the universality property. This motivated Y. Linnik and I. Ibragimov to conjecture that every Dirichlet series, with has an analytic continuation and satisfies some "growth condition" must be universal. In this talk, we will formulate this conjecture more precisely and prove some partial results towards the conjecture.