On some exponential sums involving Maass forms over arithmetic progressions (Q897529)
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scientific article; zbMATH DE number 6516860
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some exponential sums involving Maass forms over arithmetic progressions |
scientific article; zbMATH DE number 6516860 |
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On some exponential sums involving Maass forms over arithmetic progressions (English)
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7 December 2015
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Let \(g(z)\) be a Maass cusp form for \(\mathrm{SL}(2, \mathbb{Z})\), and let \(\lambda_g(n)\) be the \(n\)-th Fourier coefficient of \(g(z)\). The author studies the exponential sum \[ \mathop{\sum_{n\sim X}}_{n\equiv l (\bmod q)}\lambda_g(n)\text{e}\left(\alpha n^{\beta}\right), \] and provides some estimates and asymptotic formulas.
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Fourier coefficients of Maass forms
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exponential sums
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arithmetic progression
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