4 papers
On the problem of large gcd for disjoint residue classes
Jan Fornal, Yu-Chen Sun
Consider pairwise disjoint residue classes . We prove that \[ \max_{1\leq i<j\leq k}\gcd(m_i,m_j) \gg k\exp\!\left(-(2+o(1)) \sqrt{\frac{\log k}{\log\log k}}\ri…
Benchmarking Scientific Machine Learning Models for Air Quality Data
Khawja Imran Masud, Venkata Sai Rahul Unnam, Sahara Ali
Accurate air quality index (AQI) forecasting is essential for the protecting public health in rapidly growing urban regions, and the practical model evaluation and selection are of…
The Wiener Wintner Theorem Along the Primes
Jan Fornal, Anastasios Fragkos, Ben Krause +3
We prove the following Wiener-Wintner Theorem along the sequence of prime times, the first extension of the Wiener-Wintner Theorem to arithmetic sequences: for every probability sp…
Pointwise ergodic theorem along primes of the form
Jan Fornal
This paper resolves the question of pointwise convergence for ergodic averages of a single function along the set of polynomial values of primes of the form . Following…