Quasialgebraic Functions

TL;DR

This paper introduces quasialgebraic functions, a new class of multivalued transcendental functions that allow explicit zero counting and include all periods, bridging algebraic and transcendental function properties.

Contribution

It defines quasialgebraic functions, expanding the class of functions with explicit zero counting to include all periods, blending algebraic and transcendental characteristics.

Findings

Explicit zero counting for quasialgebraic functions

Inclusion of all periods within this new class

Bridging algebraic and transcendental function properties

Abstract

We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently rich to include all periods (integral of rational forms over algebraic cycles).