Fourier coefficients of Siegel cusp forms of degree two. (English) Zbl 0531.10031
The following theorem is proved: Let \(k\) be an even integer \(\geq 6\). Let \(f(Z)=\sum a(T)e(\text{tr }TZ)\) be a Siegel cusp form of degree two and weight \(k\). Then \(a(T)=O(| T|^{k/2-1/4+\epsilon})\) for any \(\epsilon>0\). The proof uses the fact that the considered cusp form is a linear combination of Poincaré series and the Fourier series for such a series given in U. Christian [Math. Ann. 148, 257-307 (1962; Zbl 0141.27601)].
Reviewer: M.Peters
MSC:
| 11F46 | Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms |
| 11F30 | Fourier coefficients of automorphic forms |
Citations:
Zbl 0141.27601References:
| [1] | Proc. Japan Acad 58A pp 41– (1982) |
| [2] | DOI: 10.1007/BF02054945 · Zbl 0042.32001 · doi:10.1007/BF02054945 |
| [3] | DOI: 10.1007/BF01451138 · Zbl 0141.27601 · doi:10.1007/BF01451138 |
| [4] | DOI: 10.2307/1969810 · Zbl 0066.32002 · doi:10.2307/1969810 |
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