Additive Twists of Fourier Coefficients of Modular Forms

Details Additive Twists of Fourier Coefficients of Modular Forms Additive Twists of Fourier Coefficients of Modular Forms

2012-03-20

arxiv.org/abs/1203.4526v2

Mathematics

Number Theory

20 pages; added comments and references

Scientific paper

We study sums of additively twisted Fourier coefficients of a holomorphic cusp form, a Maass cusp form, and the symmetric-square lift of a holomorphic cusp form. We obtain bounds that are uniform with respect to both the form and the terms of the additive twist. We also improve a bound on a sum of additively twisted Fourier coefficients of a holomorphic cusp form that have also been twisted by a nonlinear exponential term. This last bound is uniform with respect to the terms of the additive twist but it is not uniform with respect to the form.

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