The Lindelöf-type conjecture for triple periods of Maass forms

Let $\phi_i$ be a Hecke–Maass cusp form with spectral parameter $\lm_i$, and let $d_i$ denote its associated triple period coefficient. For every $\eps>0$, the notation $d_i\ll|\lm_i|^{\eps}$ means that the implied constant may depend on $\eps$ but not on $i$. Lindelöf-type conjecture. For any $\eps>0$ we have

$$d_i\ll|\lm_i|^{\eps}.$$

This conjecture asks for essentially bounded individual triple periods, far beyond the theorem in the paper giving an exponent $5/3$. Via the Watson formula and lower bounds for the adjoint $L$-function, it corresponds to a Lindelöf-type bound for the associated triple $L$-functions; no resolution is supplied here.