# Bounds on shifted convolution sums for Hecke eigenforms

@article{Nordentoft2022BoundsOS, title={Bounds on shifted convolution sums for Hecke eigenforms}, author={Asbj{\o}rn Christian Nordentoft and Yiannis N. Petridis and Morten Skarsholm Risager}, journal={Research in Number Theory}, year={2022} }

Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.

## One Citation

Small scale equidistribution of Hecke eigenforms at infinity

- Mathematics
- 2020

We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. We show that at scales finer than the Planck scale they do not equidistribute while at scales more…

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