Talk page
Title:
Digging below the square-root barrier: subconvexity and exponential sums
Speaker:
Abstract:
In most circumstances, proving estimates better than those tantamount to square-root cancellation for mean values of exponential sums remains a distant prospect. It is classical that this is possible for small moments of quadratic Weyl sums. In this talk, we describe progress for higher degree exponential sums associated with Vinogradov’s mean value theorem. It transpires that a natural extension of the Main Conjecture in Vinogradov’s mean value theorem delivers subconvex estimates for twisted moments at the critical exponent, and that such conclusions may be proved unconditionally in the cubic case.
Link:
Workshop: