Abstract
We estimate the spectral radius of perturbations of a particular family of composition operators, in a setting where the usual choices of norms do not account for the typical size of the perturbation. We apply this to estimate the growth rate of large moments of a Thue-Morse generating function and of the Stern sequence. This answers in particular a question of Mauduit, Montgomery and Rivat (2018).
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Acknowledgments
The authors wish to thank L. Spiegelhofer for discussions on the topics of this work, and the anonymous referee for suggestions which helped improve the manuscript.
S. Bettin is a member of the INdAM group GNAMPA and his work is partially supported by PRIN 2017 “Geometric, algebraic and analytic methods in arithmetic” and by INdAM.
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À la mémoire de Christian Mauduit
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Bettin, S., Drappeau, S. Two arithmetic applications of perturbations of composition operators. JAMA 144, 335–349 (2021). https://doi.org/10.1007/s11854-021-0184-1
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DOI: https://doi.org/10.1007/s11854-021-0184-1