Soumya Das (IISc Bangalore): Saito-Kurokawa lifts: 'mass' of pullbacks

In recent papers, Liu-Young and Blomer-Rizwan-Young investigated the so-called 'mass' of pullbacks of the Saito-Kurokawa lifts of Hecke eigenforms on $\mathrm{SL}_2(\mathbb{Z})$. Using the amplification technique, we prove that 'mass' of the pullback of the Saito-Kurokawa lift of a Hecke eigenform on $\mathrm{SL}_2(\mathbb{Z})$ of weight $k$ is bounded by $k^{1-\frac{1}{210}+\varepsilon}$. This improves the previously known bound $k$ for this quantity. We would also discuss some open questions on which some work is in (slow) progress.