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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

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

Similar Discussions: Arithmetical fucntion and distributions
  1. Modular arithmetic (Replies: 11)

  2. Arithmetic tables ? (Replies: 7)

  3. Modular arithmetic (Replies: 1)

  4. Modular arithmetic (Replies: 4)

  5. Arithmetics in Z (Replies: 3)