Pseudo-random sequences, twin primes, and twisted diophantine approximation (Manuel Hauke) скачать в хорошем качестве

Pseudo-random sequences, twin primes, and twisted diophantine approximation (Manuel Hauke)

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 https://arxiv.org/abs/2506.01736 and joint work with E. Kowalski https://arxiv.org/abs/2502.08335.