Type: Seminar

Distribution: World

Expiry: 1 Jan 2024

CalTitle1: Algebra Seminar: On some arithmetic statistics for integer matrices

Auth: alexs@desktop-h8gjltm.staff.wireless.sydney.edu.au (ashe8718) in SMS-SAML

Alina Ostafe (UNSW) is speaking in the Algebra Seminar this week. We will go out for lunch after the talk. When: Friday, 6 October, 12-1pm Where: Carslaw 173 Title: On some arithmetic statistics for integer matrices Abstract: We consider the set M_n(Z; H) of n by n matrices with integer elements of size at most H and obtain a new upper bound on the number of matrices from M_n(Z; H) with a given characteristic polynomial f \in Z[X], which is uniform with respect to f. This complements the asymptotic formula of A. Eskin, S. Mozes and N. Shah (1996) in which f has to be fixed and irreducible. We use our result to address various other questions of arithmetic statistics for matrices from M_n(Z; H), e.g. satisfying certain multiplicative relations. Some of these problems generalise those studied in the scalar case n=1 by F. Pappalardi, M. Sha, I. E. Shparlinski and C. L. Stewart (2018) with an obvious distinction due to the non-commutativity of matrices. Joint works with Kamil Bulinski and Igor Shparlinski

Calendar (ICS file) download, for import into your favourite calendar application

UNCLUTTER for printing

AUTHENTICATE to mark the scnews item as read