Year: 2026
Type: preprint
Abstract: We show that for every uniform family of affine algebraic sets, there is a formula in the parameters of the family and in $n$, expressing the cardinality of the set in the ring $\mathbb Z/n \mathbb Z$. In particular, we construct such a formula for the elliptic curves in Weierstrass normal form. These formulas are arithmetic terms: fixed finite compositions of additions, multiplications, subtractions, divisions with remainder and integer exponentiations.
Source: arXiv (Cornell University)
Author: Prunescu, Mihai
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204163554