A mean-value theorem for multiplicative functions

Indlekofer, Karl-Heinz

doi:10.1007/bf01215089

Cited by 40 publications

(15 citation statements)

References 8 publications

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“…n~x~ Using the same proof as in [11] (see (10), (11), (12), (14) and R e m a r k 3 in [11]) with x k instead of x we obtain the assertion of L e m m a 1.…”

Section: The Sum Z If(n)]mentioning

confidence: 82%

“…266--267). Since, for all k E N, ]f.(pk)[ _~ 1 as p-~ o~, we obtain, by using the same method as in [11] (pp. 266--267), By the same methods one can give sufficient conditions for (a multiplicative function) [ to be an element of ~* and l lfl I~ > 0.…”

Section: The Sum Z If(n)]mentioning

confidence: 96%

“…266--267), By the same methods one can give sufficient conditions for (a multiplicative function) [ to be an element of ~* and l lfl I~ > 0. Namely, repeating the arguments used in [11], § 4 word for word one can show that (9) …”

Section: The Sum Z If(n)]mentioning

confidence: 99%

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Properties of uniformly summable multiplicative functions

Indlekofer¹

1986

Period Math Hung

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“…n~x~ Using the same proof as in [11] (see (10), (11), (12), (14) and R e m a r k 3 in [11]) with x k instead of x we obtain the assertion of L e m m a 1.…”

Section: The Sum Z If(n)]mentioning

confidence: 82%

Section: The Sum Z If(n)]mentioning

confidence: 96%

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Properties of uniformly summable multiplicative functions

Indlekofer¹

1986

Period Math Hung

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“…There is a well-developed theory with many general results about the existence of means of arithmetic functions, see Elliott (1985); Indlekofer (1980Indlekofer ( , 1981Postnikov (1988). However, those general results do not imply the specific statements of this work.…”

mentioning

confidence: 84%

Average order in cyclic groups

Gathen¹,

Knopfmacher²,

Luca³

et al. 2004

J. Théor. Nombres Bordeaux

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Résumé. Pour chaque entier naturel n, nous déterminons l'ordre moyen α(n) deséléments du groupe cyclique d'ordre n. Nous montrons que plus de la moitié de la contributionà α(n) provient des ϕ(n)éléments primitifs d'ordre n. Il est par conséquent intéressant d'étudierégalement la fonction β(n) = α(n)/ϕ(n). Nous détermi-nons le comportement moyen de α, β, 1/β et considérons aussi ces fonctions dans le cas du groupe multiplicatif d'un corps fini.Abstract. For each natural number n we determine the average order α(n) of the elements in a cyclic group of order n. We show that more than half of the contribution to α(n) comes from the ϕ(n) primitive elements of order n. It is therefore of interest to study also the function β(n) = α(n)/ϕ(n). We determine the mean behavior of α, β, 1/β, and also consider these functions in the multiplicative groups of finite fields.

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“…In this section we shall prove the following results. [2], for a>1, and Indlekofer [7], for a>1). The following resulf> is included in Indlekofer [7].…”

mentioning

confidence: 98%