Quasialgebraic Functions
  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). 
Gal Binyamini, Dmitry Novikov, Sergei Yakovenko
math.CA math.AG math.CV math.DS