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The finite Littlewood problem in \({{\mathbb {F}}}_p\)

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Abstract

Let p be a large prime number and f(x) be an integer-valued function defined in \({\mathbb F}_p\). The Littlewood problem in \({{\mathbb {F}}}_p\) is to establish non-trivial lower bounds for the \(\ell _1\) norm of exponential sums involving f(x). In the present paper, we establish new lower bounds for exponential sums including polynomials, powers of any primitive root and subgroups of \(\mathbb {F}_p^*.\)

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Acknowledgements

The author is thankful to the referee for careful reading the paper and useful remarks.

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Authors and Affiliations

  1. Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana–Azcapotzalco, C.P. 02200, Mexico, CDMX, Mexico

    Victor Cuauhtemoc García

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  1. Victor Cuauhtemoc García
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Correspondence to Victor Cuauhtemoc García.

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The author was supported by the Proyect CB005-16 from UAM-A.

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García, V.C. The finite Littlewood problem in \({{\mathbb {F}}}_p\). Ramanujan J 47, 85–98 (2018). https://doi.org/10.1007/s11139-018-0038-3

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  • DOI: https://doi.org/10.1007/s11139-018-0038-3

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