Mathematics Seminar

We consider the problem of bounding the sup-norm of $L^2$-normalised Hecke-Laplace eigenforms $\phi_j$ on $S^3$. Along the way, we overcome the difficulty of possibly small eigenvalues in the Iwaniec-Sarnak amplifier by taking a whole space of amplifiers, given by the theta-series, on which we may use Parseval. As a consequence, we can even say something about the fourth moment $\sum_j |\phi_j(z)|^4$.