A Point-Conic Incidence Bound and Applications over 𝔽_p [article]

Ali Mohammadi, Thang Pham, Audie Warren
2022 arXiv   pre-print
In this paper, we prove the first incidence bound for points and conics over prime fields. As applications, we prove new results on expansion of bivariate polynomial images and on certain variations of distinct distances problems. These include new lower bounds on the number of pinned algebraic distances as well as improvements of results of Koh and Sun (2014) and Shparlinski (2006) on the size of the distance set formed by two large subsets of finite dimensional vector spaces over finite
more » ... . We also prove a variant of Beck's theorem for conics.
arXiv:2111.04072v2 fatcat:kotc6q5z6rcclok32abuhtwfby