Fernando Chamizo, Izabela Petrykiewicz, Serafín Ruiz-Cabello
Published 2015-04-20Version 1
In this paper we study the local regularity of fractional integrals of Fourier series using several definitions of the H\"older 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.
Comments: 18 pages, 6 pdf figures, uses .bbl file
On the regularity of fractional integrals of modular forms
Fourier series for nonperiodic functions
$\mathbf L^1$ completeness for Fourier series
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