Bulletin of the Belgian Mathematical Society - Simon Stevin

Fonctions arithmétiques multiplicativement monotones

Michel Balazard

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Abstract

A real arithmetic function $f$ is \emph{multiplicatively monotonous} if $f(mn)-f(m)$ has constant sign for $m,n$ positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian Toeplitz-multiplicative determinants.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 2 (2019), 161-176.

Dates
First available in Project Euclid: 28 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1561687559

Digital Object Identifier
doi:10.36045/bbms/1561687559

Mathematical Reviews number (MathSciNet)
MR3975822

Zentralblatt MATH identifier
07094822

Subjects
Primary: 11C20: Matrices, determinants [See also 15B36] 11N37: Asymptotic results on arithmetic functions
Secondary: 15A15: Determinants, permanents, other special matrix functions [See also 19B10, 19B14] 15B05: Toeplitz, Cauchy, and related matrices

Keywords
Sets of multiples Toeplitz-multiplicative determinants logarithmic density

Citation

Balazard, Michel. Fonctions arithmétiques multiplicativement monotones. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 2, 161--176. doi:10.36045/bbms/1561687559. https://projecteuclid.org/euclid.bbms/1561687559


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