Errata to "Average orders of multiplicative arithmetical functions of integer matrices" (Acta Arith. 66 (1994), 45-62)

We recall the well-known notion of the set of uniqueness for arithmetical functions, introduced by Kátai and several other mathematicians like Indlekofer, Elliot and Hoffman, independently. We define its analogue for completely additive complex-valued functions over the set of non-zero Gaussian integers with some examples. We show that the set of "Gaussian prime plus one's" along with finitely many Gaussian primes of norm up to some constant K is a set of uniqueness with respect to Gaussian integers. This is analogous to Kátai's result in the case of positive integers [I. Kátai, On sets characterizing number theoretical functions, II, Acta Arith.16 (1968) 1–14].

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Arithmetical Functions

10.1017/cbo9781107359963 ◽

1994 ◽

Cited By ~ 39

Author(s):

Wolfgang Schwarz ◽

Jürgen Spilker

Keyword(s):

Arithmetical Functions

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On the Modulus of Continuity of the Distribution of Some Arithmetical Functions

Analytic and Probabilistic Methods in Number Theory ◽

10.1515/9783112314234-025 ◽

1992 ◽

pp. 223-234 ◽

Cited By ~ 1

Keyword(s):

Modulus Of Continuity ◽

Arithmetical Functions

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On Some Rings of Arithmetical Functions

Georgian Mathematical Journal ◽

10.1515/gmj.1999.299 ◽

1999 ◽

Vol 6 (4) ◽

pp. 299-306

Author(s):

D. Bhattacharjee

Keyword(s):

Arithmetical Functions ◽

Algebraic Properties

Abstract In this paper we consider several constructions which from a given 𝐵-product *𝐵 lead to another one . We shall be interested in finding what algebraic properties of the ring 𝑅𝐵 = 〈𝐶ℕ, +, *𝐵〉 are shared also by the ring . In particular, for some constructions the rings 𝑅𝐵 and will be isomorphic and therefore have the same algebraic properties.

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