Squares in a Beatty sequence and an improvement on character sums
Squares in a Beatty sequence and an improvement on character sums
<title>Abstract</title> We consider the distribution of perfect squares in a Beatty sequence, which is of the form ⌊αn + β⌋. We also analyze it on average over positive square-free integers. The proof relies on a new bound of character sums with Beatty sequences, which answers an open question posted by …