题 目: Moments and equidistributions of multiplicative analogues of Kloosterman
报告人: 郗平 教授 （西安交通大学）
摘要: In this talk, we consider a family of character sums as multiplicative analogues of Kloosterman sums. We establish asymptotic formulae for any real (positive) moments of the above character sum as the character runs over all non-trivial multiplicative characters mod p, confirming a conjecture of Professor Wenpeng Zhang from 2002. Moreover, an arcsine law will be established as a consequence of the method of moments in probability theory. The arguments, amongst other tools, also allow us to obtain asymptotic formulae for moments of such character sums weighted by special L-values (at 1/2 and 1). The tools will include Gauss sums, hyper-Kloosterman sums, as well as a recent estimate for bilinear forms with general algebraic trace functions due to Fouvry, Kowalski and Michel.
All are welcome!