Comptes Rendus
no. 4
Number theory/Mathematical analysis
Note on the differentiability of arithmetic Fourier series arising from Eisenstein series

Presented by: Jean-Pierre Kahane

Izabela Petrykiewicz1
1 Université Joseph-Fourier, Institut Fourier, 100, rue des Maths, 38402 Saint-Martin-d'Hères, France
Comptes Rendus. Mathématique, Volume 352 (2014) no. 4, pp. 273-276.

The aim of this note is to present results concerning the differentiability of some Fourier series arising from Eisenstein series. Sine series exhibit different behaviours with respect to differentiability than the series with cosine function. The precise results are given for the series related to Eisenstein series of weight 2, whereas for the series arising from Eisenstein series of higher weight we conjecture the results.

Le but de cette note est de présenter des résultats concernant la dérivabilité de certaines séries de Fourier découlant des séries d'Eisenstein. Les séries de sinus se comportent différemment des séries de cosinus. Les résultats précis sont donnés pour les séries liées à la série d'Eisenstein de poids 2. Pour les séries découlant des séries d'Eisenstein de poids supérieur à 2, nous formulons une conjecture.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.02.009

Izabela Petrykiewicz 1

1 Université Joseph-Fourier, Institut Fourier, 100, rue des Maths, 38402 Saint-Martin-d'Hères, France 
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Izabela Petrykiewicz. Note on the differentiability of arithmetic Fourier series arising from Eisenstein series. Comptes Rendus. Mathématique, Volume 352 (2014) no. 4, pp. 273-276. doi : 10.1016/j.crma.2014.02.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.02.009/

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