Théorème des nombres premiers pour les fonctions digitales
Volume 165 / 2014
Acta Arithmetica 165 (2014), 11-45
MSC: 11A41, 11A63, 11L20.
DOI: 10.4064/aa165-1-2
Abstract
The aim of this work is to estimate exponential sums of the form $ \sum _{n\le x} \varLambda (n) \exp(2i\pi (f(n)+\beta n)), $ where $\varLambda $ denotes von Mangoldt's function, $f$ a digital function, and $\beta \in \mathbb {R}$ a parameter. This result can be interpreted as a Prime Number Theorem for rotations (i.e. a Vinogradov type theorem) twisted by digital functions.
