ZEROS OF CERTAIN COMBINATIONS OF EISENSTEIN SERIES

We prove that if k and l are sufficiently large, then all the zeros of the weight k + l cusp form E-k(Z)E-l(Z) - Ek+l(z) in the standard,fundamental domain lie on the boundary. We, moreover, find formulas for the number of zeros on the bottom arc with vertical bar z vertical bar = 1, and those on the sides with Re(z) = +/- 1/2. One important ingredient of the proof is an approximation of the Eisenstein series in terms of the Jacobi theta function.