# On the mean square of short exponential sums related to cusp forms

@inproceedings{ErnvallHytonen2010OnTM, title={On the mean square of short exponential sums related to cusp forms}, author={Anne-Maria Ernvall-Hytonen}, year={2010} }

The purpose of the article is to estimate the mean square of a squareroot length exponential sum of Fourier coefficients of a holomorphic cusp form.

## 5 Citations

Moments and oscillations of exponential sums related to cusp forms

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2016

Abstract We consider large values of long linear exponential sums involving Fourier coefficients of holomorphic cusp forms. The sums we consider involve rational linear twists e(nh/k) with…

Exponential sums related to Maass forms

- MathematicsActa Arithmetica
- 2019

We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of…

Mean square estimate for relatively short exponential sums involving Fourier coefficients of cusp forms

- Mathematics
- 2013

when α ∈ R. This was an improvement over the classical result by Wilton [12]. By the Rankin-Selberg mean value theorem [10] this bound is the best possible in the general case, even though for some…

A pr 2 01 5 Exponential Sums Related to Maass Forms

- Mathematics
- 2018

We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of…

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