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Everything about Möbius function
Multiplicative function in number theory
The Möbius function is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius in 1832. It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula. Following work of Gian-Carlo Rota in the 1960s, generalizations of the Möbius function were introduced into combinatorics, and are similarly denoted. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Möbius functionA 5-minute orientation
- Skim a recent paper: Möbius cancellation on polynomial sequences and the quadratic Bateman–Horn conjecture over function fieldsInfluential work since 2022
- Pick up a classic book: On the Möbius laddersThe most-reprinted book on the subject
- Read the landmark paper: The Möbius function of a latticeCited 52 times
- Go sideways: Dirichlet convolutionA closely related topic
- Go sideways: Arithmetic functionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Möbius function of a lattice
Supersymmetry and the Möbius inversion function
The Möbius function and distal flows
The distribution of the summatory function of the Möbius function
Quadratic uniformity of the Möbius function
Möbius invariant function spaces.
The Möbius function and connected graphs
Exponential Sums Formed with the Möbius Function
🆕 Influential since 2022
Möbius cancellation on polynomial sequences and the quadratic Bateman–Horn conjecture over function fields
On the Möbius function in all short intervals
Algorithms of the Möbius function by random forests and neural networks
On a generalized Möbius invariant function space
Some Operators on Minimal $$\alpha $$-Möbius Invariant Function Spaces
📚 Books worth reading
- 📕On the Möbius laddersRichard K. Guy, Frank Harary · 1966
- 📕Generalizations of the Möbius' theorem of inversionN. Negoescu · 1995
Möbius functions, incidence algebras, and power series representationsArne Dür · 1986
Möbius inversion in physicsNanxian Chen · 2010- 📕Möbius algebrasConference on Möbius Algebras University of Waterloo 1971. · 1971
Gödelsatz, Möbius-Schleife, Computer-IchKreuzer, Franz. · 1986
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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