Underlying a lot of modern number theory is the philosophy that arithmetic quantities for which no obvious reason for correlation exists should indeed be uncorrelated in a precise quantitative sense. A classical example is provided by the square-root cancellation in exponential sums such as the quadratic Gauss sums (which feature in the proof of quadratic reciprocity) or Kloosterman sums. Polygonal paths traced by their normalized incomplete sums give a fascinating insight into their chaotic formation. In this talk, we will present our recent results describing the limiting shape distribution in two ensembles of Gauss and Kloosterman sum paths as well as related results on sums of products of Kloosterman sums.
Event Date
2026-01-21
Event Time
03:15 pm ~ 04:35 pm
Event Location
Wachman 413