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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: balog@math-inst.hu
A. PERELLI
Affiliation:
Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy. E-mail: perelli@dima.unige.it
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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

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