Pseudo-random sequences, twin primes, and twisted diophantine approximation

Abstract: In this talk, I will speak about dynamics of $(a_n\alpha)_{n} \mod 1$ for integer sequences $(a_n)_n$ and fixed irrational rotations $\alpha$. The focus will be on the sequence of primes and other multiplicatively defined sequences, where gap statistics as well as twisted diophantine approximation will be considered. If time permits, I will outline the proof that includes a sieve coming from the twin prime counting problem, and establishing via random walks on Ostrowski digits an equidistribution result on diophantine Bohr sets mod d. This talk is partially based on arxiv.org/abs/2506.01736 and joint work with E. Kowalski arxiv.org/abs/2502.08335.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar