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Analytic and Diophantine properties of certain arithmetic Fourier series

Abstract : We consider certain Fourier series which arise from modular or automorphicforms. We study their analytic properties: differentiability, modulus of continuity and theH¨older regularity exponent. We use two different methods. One is based on finding anditerating a functional equation for the function studied (Itatsu’s method), the second onecomes from wavelet analysis (Jaffard’s method). The crucial steps in both of them arebased on the underlined modularity. We find that the analytic properties of these seriesat an irrational x are related to the fine diophantine properties of x, in a very precise way.The work was motivated by the study of the Riemann series.
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Izabela Petrykiewicz. Analytic and Diophantine properties of certain arithmetic Fourier series. Numerical Analysis [math.NA]. Université de Grenoble, 2014. English. ⟨NNT : 2014GRENM031⟩. ⟨tel-01196056⟩

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