Functiones et Approximatio Commentarii Mathematici

On sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(3,\mathbb Z)$

Jesse Jääsaari and Esa V. Vesalainen

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Abstract

We derive a truncated Voronoi identity for rationally additively twisted sums of Fourier coefficients of Maass forms for $\mathrm{SL}(3,\mathbb Z)$, and as an application obtain a pointwise estimate and a second moment estimate for the sums in question.

Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 2 (2017), 255-275.

Dates
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1490688027

Digital Object Identifier
doi:10.7169/facm/1632

Mathematical Reviews number (MathSciNet)
MR3732898

Zentralblatt MATH identifier
06864174

Subjects
Primary: 11L07: Estimates on exponential sums
Secondary: 11F30: Fourier coefficients of automorphic forms 11F37: Forms of half-integer weight; nonholomorphic modular forms

Keywords
exponential sums Maass forms Fourier coefficients of automorphic forms

Citation

Jääsaari, Jesse; Vesalainen, Esa V. On sums involving Fourier coefficients of Maass forms for $\mathrm{SL}(3,\mathbb Z)$. Funct. Approx. Comment. Math. 57 (2017), no. 2, 255--275. doi:10.7169/facm/1632. https://projecteuclid.org/euclid.facm/1490688027


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