Journal article
Hyper-Kloosterman sums of different moduli and their applications to automorphic forms for SLm(ℤ)
Taiwanese journal of mathematics, Vol.20(6), pp.1251-1274
2016
DOI: 10.11650/tjm.20.2016.7389
Abstract
Hyper-Kloosterman sums of different moduli appear naturally in Voronoi's summation formula for cusp forms for $\operatorname{GL}_m(\mathbb{Z})$. In this paper their square moment is evaluated and their bounds are proved in the case of consecutively dividing moduli. As an application, smooth sums of Fourier coefficients of a Maass form for $\operatorname{SL}_m(\mathbb{Z})$ against an exponential function $e(\alpha n)$ are estimated. These sums are proved to have rapid decay when $\alpha$ is a fixed rational number or a transcendental number with approximation exponent $\tau(\alpha) \gt m$. Non-trivial bounds are proved for these sums when $\tau(\alpha) \gt (m+1)/2$.
Details
- Title: Subtitle
- Hyper-Kloosterman sums of different moduli and their applications to automorphic forms for SLm(ℤ)
- Creators
- Xiumin RenYangbo Ye
- Resource Type
- Journal article
- Publication Details
- Taiwanese journal of mathematics, Vol.20(6), pp.1251-1274
- DOI
- 10.11650/tjm.20.2016.7389
- ISSN
- 1027-5487
- Language
- English
- Date published
- 2016
- Academic Unit
- Mathematics
- Record Identifier
- 9983985881102771
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