suzanne.soy/racket
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Mention that the Von Mangoldt function is not multiplicative

Browse Source
This commit is contained in:
Jens Axel Søgaard 2014-11-08 14:10:10 +01:00
parent 8f238fe9e2
commit b7d2722d7d
1 changed files with 4 additions and 2 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
pkgs/math-pkgs/math-doc/math/scribblings/math-number-theory.scrbl
View File

@ -517,9 +517,9 @@ square, otherwise @racket[#f].
} }
@; ---------------------------------------- @; ----------------------------------------
@section[#:tag "multiplicative"]{Multiplicative Functions} @section[#:tag "multiplicative"]{Multiplicative and Arithmetic Functions}
The functions in this section are @deftech{multiplicative}. The functions in this section are @deftech{multiplicative} (with exception of the Von Mangoldt function).
In number theory, a multiplicative function is a function @racket[f] such that In number theory, a multiplicative function is a function @racket[f] such that
@racket[(f (* a b)) = (* (f a) (f b))] for all coprime natural numbers @racket[a] and @racket[b]. @racket[(f (* a b)) = (* (f a) (f b))] for all coprime natural numbers @racket[a] and @racket[b].
@ -573,6 +573,8 @@ The von Mangoldt function.
If @racket[n=p^k] for a prime @racket[p] and an integer @racket[k>=1] then @racket[(log n)] is returned. If @racket[n=p^k] for a prime @racket[p] and an integer @racket[k>=1] then @racket[(log n)] is returned.
Otherwise 0 is returned. Otherwise 0 is returned.
Note: The Von Mangoldt function is not multiplicative.
@interaction[#:eval untyped-eval @interaction[#:eval untyped-eval
(mangoldt-lambda (* 3 3)) (mangoldt-lambda (* 3 3))
(log 3)] (log 3)]