报告人：Jean-Paul Allouche（CNRS/Univ. Paris ）

邀请人：胡怡宁 

报告时间：2020年12月11日（星期五）16:00-18:00

报告地点：https://us05web.zoom.us/j/86176011972?pwd=c3l6UEpTekpFOEZoaUY4MjdBVkw0UT09会议ID: 861 7601 1972 密码 : L38udu

https://us05web.zoom.us/j/84026557828?pwd=a2pYV0lCUHliZXJvZEYrQjZHR1lBdz09会议ID: 840 2655 7828 密码 : nA13bB

报告题目：Zeta-regularization of infifinite products of integers

报告摘要：Is it possible to give a “reasonable sense” to the product of all integers?We will see that an answer can be1 × 2 × 3 × ... × n × ... = √2π.After recalling the defifinition of the “zeta-regularization” of an infifinite product of positive reals, we will indicate several examples. Then we will apply this notion to defifining the product of all odious integers, i.e., of all integerswhose binary expansion contains an odd number of 1’s1 × 2 × 4 × 7 × 8 × 11 × 13 × 14 × 16 × 19 × 21 × ...and to proving that this product is equal to $\pi^{1/4}\sqrt{2\varphi e^\gamma}$, where γ and ϕ are respectively the Euler-Mascheroni and the Flajolet-Martin constants.

报告人简介：Jean-Paul Allouche is a researcher at CNRS and world expert of automatic sequences.