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Everything about Completely multiplicative function
Arithmetic function
In number theory, functions of positive integers which respect products are important and are called completely multiplicative functions or totally multiplicative functions. A weaker condition is also important, respecting only products of coprime numbers, and such functions are called multiplicative functions. Outside of number theory, the term "multiplicative function" is often taken to be synonymous with "completely multiplicative function" as defined in this article. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Completely multiplicative functionA 5-minute orientation
- Skim a recent paper: On averages of completely multiplicative functions over co-prime integer pairsInfluential work since 2022
- Pick up a classic book: Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston MaThe most-reprinted book on the subject
- Read the landmark paper: Completely multiplicative functions taking values in ${-1,1}$Cited 23 times
- Go sideways: Dirichlet convolutionA closely related topic
- Go sideways: Divisor sum identitiesA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Completely multiplicative functions taking values in ${-1,1}$
Completely q-multiplicative functions: the Mellin transform approach
Some Properties of Completely Multiplicative Arithmetical Functions
Characterizing completely multiplicative functions bygeneralized Möbius functions
Subword complexity and non-automaticity of certain completely multiplicative functions
Completely Multiplicative Automatic Functions
On consecutive values of random completely multiplicative functions
Logarithmic Operators and Characterizations of Completely Multiplicative Functions
🆕 Influential since 2022
On averages of completely multiplicative functions over co-prime integer pairs
Constructing Θ-Ξ functions via multiplicative generators on a completely distributive lattice
Completely Multiplicative Functions with Special Properties
Some multiple Dirichlet series of completely multiplicative arithmetic functions
📚 Books worth reading
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices Ams Special Session Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices January 67 2012 Boston MaRanked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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