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

Partial Summation Question

  1. Sep 9, 2009 #1
    Let [tex]k[/tex] and [tex]n \le X[/tex] be large positive integers, and [tex]p[/tex] is a prime. Define

    [tex]F(X,n) := \sum_{\substack{k^2+p = n\\X/2\le p<X\\\sqrt{X}/2 \le k < \sqrt{X}}}\log p[/tex]
    [tex]Q(n) := \sum_{k^2+p = n}\log p[/tex].

    Note that in [tex]Q(n)[/tex], the ranges of [tex]k[/tex] and [tex]p[/tex] are unrestricted.

    My question is:
    I know that [tex]F(X,n)[/tex] and [tex]Q(n)[/tex] can be related by partial summation, but how do I prove this?

    Any help is appreciated!!

  2. jcsd
  3. Sep 13, 2009 #2

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook