By exploiting the recent analytic tool of friable summation, this work describes a new approach to a class of problems in multiplicative number theory and Fourier series theory originated by H. Davenport. A definite answer to the last original question of Davenport of this type, which was still open, as well as a number of other applications, is given.
Publié le : 2004-07-05
Classification:
largest prime factor,
Fourier series,
Gibbs phenomenon,
friable integers,
multiplicative functions,
largest prime factor.,
AMS Classification: 11L07, 11N25, 11N64,
[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
@article{hal-00145883,
author = {De La Bret\`eche, R\'egis and Tenenbaum, G\'erald},
title = {S\'eries trigonom\'etriques \`a coefficients arithm\'etiques},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00145883}
}
De La Bretèche, Régis; Tenenbaum, Gérald. Séries trigonométriques à coefficients arithmétiques. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00145883/