Location and double interlacing of zeros of certain combination of the Eisenstein series for Γ+0 (2)

Abstract

We show that the zeros of aE +2 k ( z ) - ( E k + ( z )) 2 and bE +2 k ( z ) + ( E k + ( z )) 2 lie on the arc of the fundamental domain for the Fricke group Gamma + 0 (2) of level 2, where E k + ( z ) is the Eisenstein series for Gamma + 0 (2), and we investigate the doubly interlacing property between non -elliptic zeros of aE +2 k ( z ) - ( E k + ( z )) 2 and bE +2 k ( z ) + ( E k + ( z )) 2 .