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Number Theory Lunch Seminar
Additive Triples of Bijections and the Circle Method on Finite Groups
Additive Triples of Bijections and the Circle Method on Finite Groups
Organizers
Speaker
Time
Thursday, April 10, 2025 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
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.