Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T12:47:17.029Z Has data issue: false hasContentIssue false
  • English
  • Français

A NEW LOWER BOUND FOR THE L1 MEAN OF THE EXPONENTIAL SUM WITH THE MÖBIUS FUNCTION

Published online by Cambridge University Press:  01 July 1999

ANTAL BALOG  and
IMRE Z. RUZSA
ANTAL BALOG
Affiliation:
Mathematical Institute, P.O. Box 127, Budapest 1364, Hungary
IMRE Z. RUZSA
Affiliation:
Mathematical Institute, P.O. Box 127, Budapest 1364, Hungary
Get access

Abstract

The L1 means of various exponential sums with arithmetically interesting coefficients have been investigated in many recent papers. For example, Balog and Perelli proved in [1] that

formula here

for a suitable positive number c. The method of proving the lower bound in [1] is rather flexible and can work well with many multiplicative functions in place of μ(n), the Möbius function, whose Dirichlet series have a suitable expression by the Riemann ζ-function.

In this short note we improve on the above lower bound.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 415 - 418
Copyright
© The London Mathematical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)