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A NEW LOWER BOUND FOR THE L1 MEAN OF THE EXPONENTIAL SUM WITH THE MÖBIUS FUNCTION

Published online by Cambridge University Press:  01 July 1999

ANTAL BALOG  and
IMRE Z. RUZSA
ANTAL BALOG
Affiliation:
Mathematical Institute, P.O. Box 127, Budapest 1364, Hungary
IMRE Z. RUZSA
Affiliation:
Mathematical Institute, P.O. Box 127, Budapest 1364, Hungary
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Abstract

The L1 means of various exponential sums with arithmetically interesting coefficients have been investigated in many recent papers. For example, Balog and Perelli proved in [1] that

formula here

for a suitable positive number c. The method of proving the lower bound in [1] is rather flexible and can work well with many multiplicative functions in place of μ(n), the Möbius function, whose Dirichlet series have a suitable expression by the Riemann ζ-function.

In this short note we improve on the above lower bound.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 4 , July 1999 , pp. 415 - 418
Copyright
© The London Mathematical Society 1999

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