Journal article
Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
Forum mathematicum, Vol.26(1), pp.221-238
2014
DOI: 10.1515/FORM.2011.157
Abstract
Let f be a Maass cusp form for SL3(ℤ) with Fourier coefficients . We consider the sum , where . A bound better than is proved to be valid for certain transcendental numbers . This bound improves Miller's result (2006) for these α. For α close to a rational number with , the smooth sum is further proved to decay rapidly. This extends a result of Booker (2000 and 2005) on a smooth sum of without the exponential function. These bounds manifest a strange vibration nature of Maass cusp forms. The main techniques include rational approximation of real numbers, a Voronoi summation formula for SL3(ℤ), and its asymptotic expansion.
Details
- Title: Subtitle
- Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
- Creators
- Xiumin RenYangbo Ye
- Resource Type
- Journal article
- Publication Details
- Forum mathematicum, Vol.26(1), pp.221-238
- DOI
- 10.1515/FORM.2011.157
- ISSN
- 0933-7741
- eISSN
- 1435-5337
- Language
- English
- Date published
- 2014
- Academic Unit
- Mathematics
- Record Identifier
- 9983985995402771
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