On the L1 Mean of the Exponential Sum Formed with the Mobius Function |
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| Authors: | Balog A; Perelli A |
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| Institution: | Mathematical Institute of the Hungarian Academy of Sciences Reàltanoda u. 13-15, H-1364 Budapest, Hungary. E-mail: balog{at}math-inst.hu
Dipartimento di Matematica Via Dodecaneso 35, 16146 Genova, Italy. E-mail: perelli{at}dima.unige.it |
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| Abstract: | In this paper we study the L1 mean
 (1) of the exponential sum M( )= n Xµ(n)e(n), where µ(n)is the Möbius function and e(x)=e2 ix. From the Cauchy–Schwarzinequality and Parseval's identity, we have
 , (2) and it is an interesting problem to investigate whether (2)reflects the true order of magnitude of (1). |
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