The divisor function along sums of two biquadrates
Abstract
We establish power saving asymptotics for the sum of the divisor function along a binary quartic form, improving on work of Daniel. The proof involves an application of a recent two dimensional delta method due to Li, Rydin-Myerson, and Vishe and an exploitation of GL2 automorphic forms arising from the factorization of varying cubic Dedekind zeta functions.
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