Location and double interlacing of zeros of certain combination of the Eisenstein series for [formula omitted

Abstract

We show that the zeros of aE2k+(z)−(Ek+(z))2 and bE2k+(z)+(Ek+(z))2 lie on the arc of the fundamental domain for the Fricke group Γ0+(2) of level 2, where Ek+(z) is the Eisenstein series for Γ0+(2), and we investigate the doubly interlacing property between non-elliptic zeros of aE2k+(z)−(Ek+(z))2 and bE2k+(z)+(Ek+(z))2.