Rational Points on Affine Varieties over Finite Fields and Polygonal Number Sequences

Source abstract

Authors, in an earlier work, proved that prime power subsequences of the polygonal numbers corresponding to $4$, $6$, $8$, and $10$ arise naturally as the numbers of $\mathbb{F}_q$-rational points of certain double Danielewski surfaces. In this work, authors generalize the previous construction and give a new family of affine varieties over finite fields such that the number of $\mathbb{F}_q$-rational points of these varieties give the prime power subsequence of every polygonal number sequence.