Timeline for Fourier expansions in function fields
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2016 at 3:57 | vote | accept | joaopa | ||
| Apr 25, 2013 at 7:15 | comment | added | Filippo Alberto Edoardo | Well, yes, periodicity plus some convergence at cusps (to guarantee convergence at $0$ in the disk) is enough. But, again, I advise you to look at Gekeler's Inventiones paper (for this, Def. 5.6 might be what you want). | |
| Apr 25, 2013 at 5:55 | comment | added | joaopa | I thought more about a more general criteria. For example, in the classical casse, any periodic entire function on $\mathbb C$ admits a Fourier expansion. Is this the case in the function field setting? | |
| Apr 25, 2013 at 5:42 | comment | added | Filippo Alberto Edoardo | Well, as in the "classical" case, you need some condition at the cusps if you want to insist that the expansion is "integral" rather than rational. Similarly, assuming your periodic function to be a modular form, you have a notion of eigenform for which the coefficients get related to Hecke eigenvalues. In Section 6. of the paper Gekeler describes also in some detail the coefficients of Eisenstein series, but I would advise you to have a direct look at his paper. | |
| Apr 25, 2013 at 4:47 | comment | added | joaopa | Are there conditions for which f admits such an expansion? ANd when there exists a Fourier expansions, is there a formula giving the coefficients $b_a$ | |
| Apr 25, 2013 at 3:48 | history | edited | Filippo Alberto Edoardo | CC BY-SA 3.0 |
deleted 7 characters in body; edited body
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| Apr 25, 2013 at 3:40 | history | answered | Filippo Alberto Edoardo | CC BY-SA 3.0 |