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Currently displaying 1 – 12 of 12

Order by Relevance | Title | Year of publication

Infinite product representations in complex quadratic fields

Knopfmacher, Arnold — 1989

Portugaliae mathematica

A simple card guessing game revisited.

Knopfmacher, Arnold; Prodinger, Helmut — 2001

The Electronic Journal of Combinatorics [electronic only]

Two constructions of the real numbers via alternating series.

Knopfmacher, Arnold; Knopfmacher, John — 1989

International Journal of Mathematics and Mathematical Sciences

Records in set partitions.

Knopfmacher, Arnold; Mansour, Toufik; Wagner, Stephan — 2010

The Electronic Journal of Combinatorics [electronic only]

Metric properties of alternating Lüroth series

Kalpazidou, Sofia; Knopfmacher, Arnold; Knopfmacher, John — 1991

Portugaliae mathematica

A New Infinite Product Representation for Real Numbers.

Arnold Knopfmacher; John Knopfmacher — 1987

Monatshefte für Mathematik

Metric properties of some special p-adic series expansions

Arnold Knopfmacher; John Knopfmacher — 1996

Acta Arithmetica

Non-normality of continued fraction partial quotients modulo q

Arnold Knopfmacher; D. S. Lubinsky — 1990

Revista colombiana de matematicas

Lüroth-type alternating series representations for real numbers

Sofia Kalpazidou; Arnold Knopfmacher; John Knopfmacher — 1990

Acta Arithmetica

"Factorisatio numerorum" in arithmetical semigroups

Arnold Knopfmacher; John Knopfmacher; Richard Warlimont — 1992

Acta Arithmetica

Metric properties of Engel series expansions of Laurent series

Peter J. Grabner; Arnold Knopfmacher — 1998

Mathematica Slovaca

Average order in cyclic groups

Joachim von zur Gathen; Arnold Knopfmacher; Florian Luca; Lutz G. Lucht; Igor E. Shparlinski — 2004

Journal de Théorie des Nombres de Bordeaux

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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