Rational period functions in higher level cases

Extending Knopp's results [9] and [10] we investigate examples and properties of rational period functions in higher level cases, including location of poles and behavior under the action of Hecke operators. More precisely, we prove that a rational period function may have poles only at 0 or at real quadratic irrationalities. Moreover by applying the action of Hecke operators we prove that for positive odd integer k   and p∈{2,3}p∈{2,3}, the space of all rational period functions of weight 2k   for Γ0+(p) is infinite dimensional.