The first negative eigenvalue of Yoshida lifts

Abstract

We prove that for any given $$\epsilon >0$$ , the first negative eigenvalue of the Yoshida lift F of a pair of elliptic cusp forms f, g having square-free levels (where g has weight 2 and satisfies $$(\log Q_{g})^2 \ll \log Q_f$$ ), occurs before $$c_{\epsilon } \cdot Q_F^{1/2-2 \theta + \epsilon }$$ ; where $$Q_F,Q_f,Q_g$$ are the analytic conductors of F, f, g respectively, $$\theta < 1/4$$ , and $$c_{\epsilon }$$ is a constant depending only on $$\epsilon $$ .