"Linear exponential sums over primes in short intervals"

---

Let f denote either the Möbius function or the von Mangoldt function, and let α ∈ [0, 1]. I will discuss estimates for exponential sums of the form

 

 

∑x<n≤x+Hf(n)e(nα)

 

with particular emphasis on the short interval regime H<x and discuss how small H can be taken. Such estimates play a key role in studying Diophantine equations whose variables are restricted to primes in the interval [x, x + H], as well as in other arithmetic questions. This talk is based on several recent joint works with Kaisa Matomäki, Mayank Pandey, Javier Pliego, and Joni Teräväinen.

---

Download ICS Download invitation