On the modular structure of Kloosterman sums after Katz

Abstract: It is widely believed that Kloosterman sums should behave randomly in certain suitable families, and it is particularly difficult in the horizontal sense. Motivated by deep observations on elliptic curves, Nicholas Katz proposed three problems on sign change, equidistribution and modular structure of Kloosterman sums in 1980. In this talk, we will focus on the modular structures and present some recent progresses towards this problem made by analytic number theory combining certain tools from $\ell$-adic cohomology.

number theory

Audience: researchers in the topic

Number theory during lockdown

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