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The generalized divisor problem and the Riemann hypothesis

Published online by Cambridge University Press:  22 January 2016

Hideki Nakaya
Hideki Nakaya*
Affiliation:
Department of Mathematics, Kanazawa University, Kanazawa 920, Japan
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Let dz(n) be a multiplicative function defined by

where s = σ + it, z is a. complex number, and ζ(s) is the Riemann zeta function. Here ζz(s) = exp(z log ζ(s)) and let log ζ(s) take real values for real s > 1. We note that if z is a natural number dz(n) coincides with the divisor function appearing in the Dirichlet-Piltz divisor problem, and d-1(n) with the Möbious function.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 122 , June 1991 , pp. 149 - 159
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

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