Saurabh Singh (IIT Kanpur): Sum of $\mathrm{GL}(3)$ coefficients over quadratic forms

Abstract: In this talk, we consider the sum of Fourier coefficients over a quadratic form $Q(m, n)$. Namely, we consider the sum:

$$S= \sum_{m, n \sim X}  A(1, Q(m, n)),$$

where the $A(r, n)$'s are the Fourier coefficients of an $\mathrm{SL}(3,\mathbb{Z})$ Maass cusp form or the minimal Eisenstein series. Using Jutila's circle
method, we will show a non-trivial cancellation in the sum $S$.

The estimated duration of the talk is 60 minutes.