Event Series
Event Type
Seminar
Friday, April 16, 2021 11:00 AM
Emmett Wyman (Northwestern)

Abstract: Given two Laplace eigenfunctions $e_\lambda$ and $e_\mu$ of frequencies $\lambda$ and $\mu$, at what frequencies does the spectral mass of the product $e_\lambda e_\mu$ tend to lie? This problem originated in the number theoretic setting with an aim towards the resolution of the Lindel\"of hypothesis for Rankin-Selberg zeta functions. The Riemannian version of this problem has some bearing on the validity of fast algorithms for electronic structure computing and has been the subject of a recent string of papers.

Here, we describe the relationship between the Fourier coefficients $\langle e_\lambda e_\mu, e_\nu \rangle$ of the product $e_\lambda e_\mu$ and the size of a configuration set of Euclidean triangles with side lengths $\lambda$, $\mu$, and $\nu$. As a corollary, we refine a result by Lu, Sogge, and Steinerberger.

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