Jake Chinis: Siegel zeros and Sarnak's Conjecture
Time: Fri 2021-06-18 15.00 - 16.00
Lecturer: Jake Chinis (McGill University)
Location: Zoom, meeting ID: 696 8725 5050
In this talk, we will study the relationship between Siegel zeros and the Liouville function. More precisely, we will discuss how the existence of Siegel zeros implies Chowla's Conjecture on k-point correlations of the Liouville function, along a subsequence. This extends work of Germán and Kátai, where they studied the case k=2 under identical hypotheses. Then, we will briefly discuss an argument due to Sarnak, which allows us to conclude that Sarnak's Conjecture on Möbius disjointness holds, again restricted to some subsequence and assuming the existence of Siegel zeros. Our main tool is a result due to Germán and Kátai, in the same spirit of Heath-Brown's work on Siegel zeros and the Twin Prime Conjecture, which tells us that the Liouville function is well-approximated by real, primitive Dirichlet characters on "large" primes.