Fonctions arithm\'etiques multiplicativement monotones
Michel Balazard (I2M)
TL;DR
This paper investigates multiplicatively monotonous functions, exploring their properties and providing examples, with applications to determinants of positive hermitian Toeplitz-multiplicative matrices.
Contribution
It introduces the concept of multiplicatively monotonous functions, analyzes their properties, and applies these findings to specific determinants in matrix theory.
Findings
Characterization of multiplicatively monotonous functions
Examples illustrating these functions
Application to Toeplitz-multiplicative determinants
Abstract
A real arithmetic function f is 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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Graph theory and applications · Analytic Number Theory Research