Zeta functions of equivalence relations over finite fields

ABSTRACT. We prove the rationality of the generating function associated to the number of equivalence classes of Fqk -points of a constructible equivalence relation defined over the finite field Fq. This is a consequence of the rationality of Weil zeta functions and of first-order formulas, together with the existence of a suitable parameter space for constructible families of constructible sets.

• Type: Journal
• Year: 2011
• Where: FFA
• Authors: Tibor Beke
• Keywords: Constructible Equivalence Relation, FFA 2011, Weil Zeta Functions, finite field Fq