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Additive Triples of Bijections and the Circle Method on Finite Groups

组织者

文鏞碩 , 清水浩二

演讲者

吴冬生

时间

2025年04月10日 12:15 至 13:00

地点

A4-1

摘要

Let \( G \) be a finite group of order \( n \), and let \( S \) be the set of all bijections from \( \{1, 2, \dots, n\} \) to \( G \). We say that three bijections \( \pi_1, \pi_2, \pi_3 \in S \) form an *additive triple* if \( \pi_1 + \pi_2 = \pi_3 \). In this talk, we explore how ideas from analytic number theory—particularly the circle method—can be adapted to estimate the number of such additive triples.