[Note sur la dérivabilité de séries arithmétiques de Fourier provenant des séries d'Eisenstein]
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.
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.
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@article{CRMATH_2014__352_4_273_0,
author = {Petrykiewicz, Izabela},
title = {Note on the differentiability of arithmetic {Fourier} series arising from {Eisenstein} series},
journal = {Comptes Rendus. Math\'ematique},
pages = {273--276},
publisher = {Elsevier},
volume = {352},
number = {4},
year = {2014},
doi = {10.1016/j.crma.2014.02.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.02.009/}
}
TY - JOUR AU - Petrykiewicz, Izabela TI - Note on the differentiability of arithmetic Fourier series arising from Eisenstein series JO - Comptes Rendus. Mathématique PY - 2014 SP - 273 EP - 276 VL - 352 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.02.009/ DO - 10.1016/j.crma.2014.02.009 LA - en ID - CRMATH_2014__352_4_273_0 ER -
%0 Journal Article %A Petrykiewicz, Izabela %T Note on the differentiability of arithmetic Fourier series arising from Eisenstein series %J Comptes Rendus. Mathématique %D 2014 %P 273-276 %V 352 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.02.009/ %R 10.1016/j.crma.2014.02.009 %G en %F CRMATH_2014__352_4_273_0
Petrykiewicz, Izabela. Note on the differentiability of arithmetic Fourier series arising from Eisenstein series. Comptes Rendus. Mathématique, Tome 352 (2014) no. 4, pp. 273-276. doi : 10.1016/j.crma.2014.02.009. http://www.numdam.org/articles/10.1016/j.crma.2014.02.009/
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