Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T03:40:52.281Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE L1 MEAN OF THE EXPONENTIAL SUM FORMED WITH THE MÖBIUS FUNCTION

Published online by Cambridge University Press:  01 April 1998

A. BALOG  and
A. PERELLI
A. BALOG
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences, Reàltanoda u. 13-15, H-1364 Budapest, Hungary. E-mail: [email protected]
A. PERELLI
Affiliation:
Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy. E-mail: [email protected]
Get access

Abstract

In this paper we study the L1 mean

formula here

of the exponential sum M(α)= [sum ]n[les ]Xμ(n)e(nα), where μ(n) is the Möbius function and e(x)=e2πix. From the Cauchy–Schwarz inequality and Parseval's identity, we have

formula here

and it is an interesting problem to investigate whether (2) reflects the true order of magnitude of (1).

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 275 - 288
Copyright
The London Mathematical Society 1998

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.)