On multiplicative functions which are additive on sums of primes

Dubickas, Artūras; Šarka, Paulius

doi:10.1007/s00010-012-0156-8

Cited by 17 publications

(9 citation statements)

References 9 publications

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“…As was in [5], Spiro showed that if the multiplicative function f : N → C satisfies f (p + q) = f (p) + f (q) for all primes p, q and there exists n 0 ∈ N such that f (n 0 ) = 0, then f (n) = n for all n. Later, Fang [6] extended the conclusion to the equation f (p + q + r) = f (p) + f (q) + f (r). Dubickas et al [1] improved the conclusion to general case f (p…”

Section: Introductionmentioning

confidence: 88%

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

You¹,

Chen²,

Yuan³

2016

Preprint

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Section: Introductionmentioning

confidence: 88%

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

You¹,

Chen²,

Yuan³

2016

Preprint

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“…Fang [5] showed that the additive condition for primes can be changed to three primes. Also, Dubickas and Šarka [3] extended the result to the arbitrary many primes. That is, the condition can be changed to…”

Section: Introductionmentioning

confidence: 88%

$k$-additive uniqueness of the set of squares for multiplicative functions

Park¹

2016

Preprint

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P. V. Chung showed that there are many multiplicative functions f which satisfy f (m 2 + n 2 ) = f (m 2 ) + f (n 2 ) for all positive integers m and n. In this article, we show that if more than 2 squares in the additive condition are involved, then such f is uniquely determined. That is, if a multiplicative function f satisfiesk ) for arbitrary positive integers a i , then f is the identity function. In this sense, we call the set of all posotive squares a k-additive uniqueness set for multiplicative functions.

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“…Fang [5] showed that the additive condition for primes can be changed to three primes. Also, Dubickas anď Sarka [3] extended the result to the arbitrary many primes. That is, the condition can be changed to…”

Section: Introductionmentioning

confidence: 89%

On k-additive uniqueness of the set of squares for multiplicative functions

Park

2017

Aequat. Math.

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Abstract. P. V. Chung showed that there are many multiplicative functions f which satisfy f (m 2 + n 2 ) = f (m 2 ) + f (n 2 ) for all positive integers m and n. In this article, we show that if more than 2 squares in the additive condition are involved, then such f is uniquely determined. That is, if a multiplicative function f satisfiesk ) for arbitrary positive integers a i , then f is the identity function. In this sense, we call the set of all posotive squares a k-additive uniqueness set for multiplicative functions.

show abstract

On multiplicative functions which are additive on sums of primes

Cited by 17 publications

References 9 publications

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

A characterization of arithmetic functions satisfying $f(u^{2}+kv^{2})=f^{2}(u)+kf^{2}(v)$

$k$-additive uniqueness of the set of squares for multiplicative functions

On k-additive uniqueness of the set of squares for multiplicative functions

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