Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Arithmetical fucntion and distributions

  1. Mar 27, 2010 #1
    can any Arithmetical function [tex] A(x)= \sum_{n\le x}a(n) [/tex]

    be regarded as the train of dirac delta functions (its derivative)

    [tex] dA = \sum_{n=1}^{\infty}a(n)\delta (x-n) [/tex]

    from this definition could we regard the explicit formulae for chebyshev function

    [tex] d\Psi(x) =1- \sum_{\rho}x^{\rho -1}- (x^{3}-x)^{-1} [/tex]

    and from this, using the definition of Mellin transform, we could obtain the sums over the Riemann zeros for lots of function f(x) provided its Mellin transform exists.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Threads for Arithmetical fucntion distributions Date
I Fundamental Theorem of Arithmetic - Bhattacharya et al Sep 4, 2016
Gram matrix distributions Nov 24, 2015
Arithmetic mean complex numbers Jun 20, 2013
Modular Arithmetic and Diophantine Equations Oct 25, 2012
Question about arithmetic May 17, 2012