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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
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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- The London Mathematical Society 1998
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