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We prove sub-convex bounds on the fourth moment of Hecke-Laplace eigenformson $S^3$. As a corollary, we get a bound on the sup-norm on an individualeigenform, which constitutes an improvement over what is achievable throughemploying the Iwaniec-Sarnak amplifier.

Sup-norm of Hecke-Laplace Eigenforms on $S^3$