hal-00131532, version 2
Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3
Abstract: We consider logarithmic averages, over friable integers, of non-negative multiplicative functions. Under logarithmic, one-sided or two-sided hypotheses, we obtain sharp estimates that improve upon known results in the literature regarding both the quality of the error term and the range of validity. The one-sided hypotheses correspond to classical sieve assumptions. They are applied to provide an effective form of the Gallagher-Selberg prime power sieve.
- 1:
- CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- Domain : Mathematics/Number Theory
- Keywords : mean value of arithmetic functions – weighted mean values – logarithmic mean values – friable integers – sieve – Selberg sieve – Ghallager sieve – prime power sieve.
- Comment : À paraître dans Compositio Mathematica.
- Available versions : v1 (2007-02-16) v2 (2007-04-06) v3 (2007-05-10) v4 (2008-07-20)
- hal-00131532, version 2
- http://hal.archives-ouvertes.fr/hal-00131532
- oai:hal.archives-ouvertes.fr:hal-00131532
- From:
- Submitted on: Friday, 6 April 2007 16:41:19
- Updated on: Friday, 6 April 2007 16:52:54
Associated documents
Export