Journal article
Resonance between automorphic forms and exponential functions
Science China Mathematics, Vol.53(9), pp.2463-2472
09/2010
DOI: 10.1007/s11425-010-3150-4
Abstract
Let f be a holomorphic cusp form of weight k for SL 2(ℤ) and λ f (n) its n-th Fourier coefficient. In this paper, the exponential sum Σ X < n ⩽ 2X λ f (n)e(αn B ) twisted by Fourier coefficients λ f (n) is proved to have a main term of size |λ f (q)|X 3/4 when β = 1/2 and α is close to $$ \pm 2\sqrt q ,q \in \mathbb{Z} $$ , and is smaller otherwise for β < 3/4. This is a manifestation of the resonance spectrum of automorphic forms for SL 2(ℤ).
Details
- Title: Subtitle
- Resonance between automorphic forms and exponential functions
- Creators
- XiuMin Ren - School of Mathematics Shandong University Jinan 250100 ChinaYangBo Ye - Department of Mathematics The University of Iowa Iowa City Iowa 52242-1419 USA
- Resource Type
- Journal article
- Publication Details
- Science China Mathematics, Vol.53(9), pp.2463-2472
- DOI
- 10.1007/s11425-010-3150-4
- ISSN
- 1674-7283
- eISSN
- 1869-1862
- Publisher
- SP Science China Press; Heidelberg
- Language
- English
- Date published
- 09/2010
- Academic Unit
- Mathematics
- Record Identifier
- 9983985962602771
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