Fred Tyrrell

The Erdös Discrepancy Problem for Exponential Sums

In this talk, we will discuss ongoing work on when an exponential sum with multiplicative coefficients can be bounded. Our main result is a rigidity theorem, which says that in some sense the only way for such sums to be bounded is when our function is very close to being periodic. We will give an overview of how we combine a breakthrough result of Tao with a sieve theoretic technique based on work of Klurman, Mangerel, Pohoata and Teräväinen known as the 'rotation trick' to prove our main theorem.