### Abstract

We determine, up to a constant factor, the L^{1} mean of the exponential sum formed with the r-free integers. This improves earlier results of Brüdern, Granville, Perelli, Vaughan and Wooley. As an application, we improve the known bound for the L^{1} norm of the exponential sum defined with the Möbius function.

Original language | English |
---|---|

Pages (from-to) | 219-230 |

Number of pages | 12 |

Journal | Acta Mathematica Hungarica |

Volume | 90 |

Issue number | 3 |

Publication status | Published - 2001 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Acta Mathematica Hungarica*,

*90*(3), 219-230.

**On the exponential sum over r-free integers.** / Balog, A.; Ruzsa, I.

Research output: Contribution to journal › Article

*Acta Mathematica Hungarica*, vol. 90, no. 3, pp. 219-230.

}

TY - JOUR

T1 - On the exponential sum over r-free integers

AU - Balog, A.

AU - Ruzsa, I.

PY - 2001

Y1 - 2001

N2 - We determine, up to a constant factor, the L1 mean of the exponential sum formed with the r-free integers. This improves earlier results of Brüdern, Granville, Perelli, Vaughan and Wooley. As an application, we improve the known bound for the L1 norm of the exponential sum defined with the Möbius function.

AB - We determine, up to a constant factor, the L1 mean of the exponential sum formed with the r-free integers. This improves earlier results of Brüdern, Granville, Perelli, Vaughan and Wooley. As an application, we improve the known bound for the L1 norm of the exponential sum defined with the Möbius function.

UR - http://www.scopus.com/inward/record.url?scp=26444450051&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26444450051&partnerID=8YFLogxK

M3 - Article

VL - 90

SP - 219

EP - 230

JO - Acta Mathematica Hungarica

JF - Acta Mathematica Hungarica

SN - 0236-5294

IS - 3

ER -