No abstract

For k < , let E k (z) and E (z) be Eisenstein series of weights k and , respectively, for SL 2 (Z). We prove that between any two zeros of E k (e iθ ) there is a zero of E (e iθ ) on the interval π/2 < θ < 2π/3.

Let $j_n$ be the modular function obtained by applying the nth Hecke operator on the classical j-invariant. For $n>m\ge 2$ , we prove that between any two zeros of $j_m$ on the unit circle of the fundamental domain, there is a zero of $j_n$ .