We give a lower bound of the number of zeros of the modular forms $E_k^{+}{E}_{\ell }^{+}-E_{k+\ell }^{+}$ 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 ${\mathrm{\Gamma }}_0^{+}(2)$, where $E_k^{+}$ is the Eisenstein series of weight k for ${\mathrm{\Gamma }}_0^{+}(2)$.

中文翻译：

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爱森斯坦级数的某些组合的零数。 ${\mathrm{\Gamma }}_0^{+}（2）$

我们给出了模块化形式的零个数的下限 ${Ë}_{ķ}^{+}{Ë}_{\ell }^{+}-{Ë}_{ķ+\ell }^{+}$对于Fricke组，在每个弧边界和基本域的垂直边界上都有足够大的k和ℓ${\mathrm{\Gamma }}_0^{+}（2）$，在哪里 ${Ë}_{ķ}^{+}$是Eisenstein级数重量的ķ为${\mathrm{\Gamma }}_0^{+}（2）$。