The number of zeros of certain combinations of the Eisenstein series for Gamma(+)(0)(2)

Abstract

We give a lower bound of the number of zeros of the modular forms E-k(+) E-l(+) - E-k+l(+) for large enough k and l on each of the arc boundary and on the vertical boundary of the fundamental domain for the Fricke group Gamma(+)(0)(2), where E-k(+) is the Eisenstein series of weight k for Gamma(+)(0)(2).