Multiplicative functions over the Gaussian integers with regularity properties
The authors study completely multiplicative functions F defined on the multiplicative semigroup \(G^*\) of the nonzero Gaussian integers. They give a partial answer to the following question. Which functions F satisfy the condition \(F(\alpha +\gamma)-F(\alpha)\to 0\) \((\alpha,\gamma \in G^*\), \(\gamma\) arbitrary but fixed, \(| \alpha | \to \infty)\) ?
scientific article; zbMATH DE number 3995759