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math.DS2024
On quantum ergodicity for higher dimensional cat maps
Pär Kurlberg, Alina Ostafe, Zeev Rudnick +1
We study eigenfunction localization for higher dimensional cat maps, a popular model of quantum chaos. These maps are given by linear symplectic maps in ${\mathrm{Sp}}(2g,\mathbb Z…
math.NT2024
On the frequency of primes preserving dynamical irreducibility of polynomials
Alina Ostafe, Igor E. Shparlinski
Towards a well-known open question in arithmetic dynamics, L. Mérai, A. Ostafe and I. E. Shparlinski (2023), have shown, for a class of polynomials , which in p…
math.NT2024
Statistics of ranks, determinants and characteristic polynomials of rational matrices
Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe +1
We consider the set of matrices with rational entries having numerator and denominator of size at most and obtain upper and lower bounds on the number of such matri…