The finite Littlewood problem in $${{\mathbb {F}}}_p$$ |
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Authors: | Victor Cuauhtemoc García |
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Institution: | 1.Departamento de Ciencias Básicas,Universidad Autónoma Metropolitana–Azcapotzalco,Mexico,Mexico |
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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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