标题：On the distinction between Kloosterman sums and multiplicative functions
时间：星期一，15:00-16:00， 10月20日， 2025
地点：8A306
主持人：何子龙
摘要：The Kloosterman sum Kl(a,c) is one of the most important objects in analytic number theory. It is generally believed that Kl(a,c) as an arithmetic function is not far away from being a multiplicative function. In this talk, I will challenge this belief. More precisely, fix any integers a\not=0 and k>1, for any given nonzero complex number \eta and complex valued multiplicative function f, we will show that 100% of the square-free k-almost primes n satisfy Kl(a,n)\not=\eta f(n).
In the first half of the talk, I will recall some basic results on Kloosterman sums, and report some recent progress on the distribution of Kl(a,c) at almost prime moduli c. In the second half, I will introduce our results and give a sketch of the proofs.
嘉宾简介：
张扬, 西安交通大学博士生, 研究方向是二次型的算术理论、丢番图分析和代数指数和. 目前有一篇论文发表于《Trans. Amer. Math. Soc.》.
（撰稿、 一审：何子龙， 二审：余馥凝， 终审： 陶铭）
