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The Hölder exponent of some Fourier series

2015/04/20 by Fernando Chamizo, Chamizo, Fernando, Izabela Petrykiewicz +3
Mathematics · #11F30 #26A16 #28A80 #42A16 #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #math.CA #msc:11F30 #msc:26A16 #msc:28A80 #msc:42A16

paper · pdf · doi:10.48550/arxiv.1504.04998

18 pages, 6 pdf figures, uses .bbl file

arxiv created 2015/04/20 · openalex publication_date 2015/04/20 · arxiv updated 2015/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the local regularity of fractional integrals of Fourier series using several definitions of the Hölder exponent. We especially consider series coming from fractional integrals of modular forms. Our results show that in general cusp forms give rise to pure fractals (as opposed to multifractals). We include explicit examples and computer plots.

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