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The generalized divisor problem and the Riemann hypothesis
Published online by Cambridge University Press: 22 January 2016
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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.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1991
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