Seminar series
Date
Thu, 18 Jan 2024
16:00
16:00
Location
Lecture Room 4, Mathematical Institute
Speaker
Ofir Gorodetsky
Organisation
University of Oxford
Let g be a matrix chosen uniformly at random from the GL_n(F_q), where F_q is the field with q elements. We consider two questions:
1. For fixed k and growing n, how fast does Tr(g^k) converge to the uniform distribution on F_q?
2. How large can k be taken, as a function of n, while still ensuring that Tr(g^k) converges to the uniform distribution on F_q?
We will answer these two questions (as well as various variants) optimally. The questions turn out to be strongly related to the study of particular character sums in function fields.
Based on joint works with Brad Rodgers (arXiv:1909.03666) and Valeriya Kovaleva (arXiv:2307.01344).