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Journal Articles Acta Arithmetica Year : 2015

Fonctions digitales le long des nombres premiers

Abstract

The aim of this work is to estimate exponential sums of the form Σn≤xΛ(n) exp(2iπ(f(n) + βn)), where Λ denotes von Mangoldt's function, f a digital function, and β ∈ double-struck R a parameter. This result can be interpreted as a Prime Number Theorem for rotations (i.e. a Vinogradov type theorem) twisted by digital functions.

Dates and versions

hal-01259963 , version 1 (21-01-2016)

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Bruno Martin, Christian Mauduit, Joel Rivat. Fonctions digitales le long des nombres premiers. Acta Arithmetica, 2015, 170 (2), pp.175-197. ⟨10.4064/aa170-2-5⟩. ⟨hal-01259963⟩
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