CP-violation in neutrino oscillations and L/E flatness of the e-like event ratio at Super-Kamiokande

We show that if the presently observed L/E-flatness of the electron-like event ratio in the Super-Kamiokande atmospheric neutrino data is confirmed, then the indicated ratio must be unity. Further, it is found that once CP is violated the exact L/E flatness implies: (a) the CP-violating phase, in the standard parametrization, is narrowed down to two possibilities +/-pi/2, and (b) the mixing between the second and the third generations must be maximal. With these results at hand, we argue that a dedicated study of the L/E-flatness of the electron-like event ratio by Super-Kamiokande can serve as an initial investigatory probe of CP violation in the neutrino sector. The assumptions under which these results hold are explicitly stated.