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

  • A. BALOG (a1) and A. PERELLI (a2)

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).

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