Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2001
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2001

[Date Index] [Thread Index] [Author Index]

Search the Archive

Dirichlet generating function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg26551] Dirichlet generating function
  • From: "Arnold Knopfmacher" <arnoldk at cam.wits.ac.za>
  • Date: Fri, 5 Jan 2001 00:34:02 -0500 (EST)
  • Organization: MS, University of the Witwatersrand
  • Sender: owner-wri-mathgroup at wolfram.com

I wish to expand the product 
Product[1/(1-n^(-s)),{n,2,12}] to obtain output in the form of a Dirichlet series,
1+2^(-s)+3^(-s)+2*4^(-s)+5^(-s)+2*6^(-s)+...4*12^(-s)+...

(The coefficients of m^(-s) in the above series give the number of
factorizations of m into factors greater than 1. E.g. 12 can be factored
in 4 ways, as 12 or 6*2 or 4*3 or 3*2*2).

Thanks


Arnold Knopfmacher
Dept of Computational and Applied Maths
Witwatersrand University
Johannesburg 2050
South Africa
http://www.wits.ac.za/science/number_theory/arnold.htm
Fax: 2711-4039317
Phone: 2711- 717-6121
email: arnoldk at gauss.cam.wits.ac.za


  • Prev by Date: Importing .eps files on a Mac
  • Next by Date: Bus error in kernel
  • Previous by thread: Importing .eps files on a Mac
  • Next by thread: Re: Dirichlet generating function