Functiones et Approximatio Commentarii Mathematici

Sommes d'exponentielles friables d'arguments rationnels

Gérald Tenenbaum and Régis de la Bretèche

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Let $\mathcal{M}$ denote the class of multiplicative functions with values in the unit disk, and, for $x\geq 1$, $y\geq 1$, let $S(x,y)$ designate the set of $y$-friable positive integers not exceeding $x$. We provide, as $x$ and $y$ tend to infinity in prescribed ranges, upper bounds for exponential sums of the form $$E_f(x,y;\vartheta):=\sum_{n\in S(x,y)}f(n)\hbox{\rm e}^{2\pi i n\vartheta}$$ whenever $f\in \mathcal{M}$ and $\vartheta$ is a rational number with denominator not exceeding a fixed power of $\log x$.

Article information

Funct. Approx. Comment. Math., Volume 37, Number 1 (2007), 31-38.

First available in Project Euclid: 18 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11L03: Trigonometric and exponential sums, general
Secondary: 11L07: Estimates on exponential sums 11N25: Distribution of integers with specified multiplicative constraints 11N37: Asymptotic results on arithmetic functions

friable integers exponential sums exponential sums with multiplicative coefficients


de la Bretèche, Régis; Tenenbaum, Gérald. Sommes d'exponentielles friables d'arguments rationnels. Funct. Approx. Comment. Math. 37 (2007), no. 1, 31--38. doi:10.7169/facm/1229618739.

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