Motivated by deep observations on elliptic curves/modular forms, Nicholas Katz proposed three problems on sign changes, equidistributions and modular structures of Kloosterman sums in 1980. In this talk, we will discuss some recent progresses towards these three problems made by analytic number theory (e.g., sieve methods and automorphic forms) combining certain tools from ℓ-adic cohomology.
This video is part of the Number Theory Web Seminar series.
