Another generalization of the gcd-sum function

Abstract

We investigate an arithmetic function representing a generalization of the gcd-sum function, considered by Kurokawa and Ochiai in 2009 in connection with the multivariable global Igusa zeta function for a finite cyclic group. We show that the asymptotic properties of this function are closely connected to the Piltz divisor function. A generalization of Menon's identity is also considered.

9 pages

References in corpus (5)

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• A generalization of Menon's identity
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Cited by in corpus (4)

• Proofs, generalizations and analogs of Menon's identity: a survey
• Menon-type identities concerning additive characters
• Almost-primes in horospherical flows on the space of lattices
• Menon-type identities concerning Dirichlet characters