# On the Properties of the Möbius Function

Formalized Mathematics (2006)

• Volume: 14, Issue: 1, page 29-36
• ISSN: 1426-2630

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## Abstract

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We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is very much like the one developed in Isabelle proof assistant connected with Avigad's formal proof of Prime Number Theorem) was done according to the book [13].

## How to cite

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Magdalena Jastrzebska, and Adam Grabowski. "On the Properties of the Möbius Function." Formalized Mathematics 14.1 (2006): 29-36. <http://eudml.org/doc/266801>.

@article{MagdalenaJastrzebska2006,
abstract = {We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is very much like the one developed in Isabelle proof assistant connected with Avigad's formal proof of Prime Number Theorem) was done according to the book [13].},
author = {Magdalena Jastrzebska, Adam Grabowski},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {29-36},
title = {On the Properties of the Möbius Function},
url = {http://eudml.org/doc/266801},
volume = {14},
year = {2006},
}

TY - JOUR
AU - Magdalena Jastrzebska
TI - On the Properties of the Möbius Function
JO - Formalized Mathematics
PY - 2006
VL - 14
IS - 1
SP - 29
EP - 36
AB - We formalized some basic properties of the Möbius function which is defined classically as [...] as e.g., its multiplicativity. To enable smooth reasoning about the sum of this number-theoretic function, we introduced an underlying many-sorted set indexed by the set of natural numbers. Its elements are just values of the Möbius function.The second part of the paper is devoted to the notion of the radical of number, i.e. the product of its all prime factors.The formalization (which is very much like the one developed in Isabelle proof assistant connected with Avigad's formal proof of Prime Number Theorem) was done according to the book [13].
LA - eng
UR - http://eudml.org/doc/266801
ER -

## References

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