## Number Theory Seminar

### Thursday, November 7th, 2019

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

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

**Title:** On the distribution of certain sequences and a prime number theorem.

**Abstract:** The fourth problem of Landau conjectures that there are infinitely many primes of the form $n^2+1$. Inspired by this, we consider sequences of the form $\{[n^{\alpha}] + 1\}$, where $[x]$ denotes the greatest integer less than or equal to $x$. In this talk, we will discuss how often the elements of such a sequence lie in a given arithmetic progression for $\alpha<2$ and also establish an analogue of prime number theorem for $\alpha<1$. This is joint work with Prof. M. Ram Murty.