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

Sum of 4 squares and Riemann zeros

  1. Feb 9, 2007 #1
    Hello,

    I need help with the following :

    Jacobi showed that the number of solutions to w2+x2+y2+z2=n (all inetegers) is given by A(n) = 8*sum of divisors of n not divisible by 4
    (see sloane's sequence
    http://www.research.att.com/~njas/sequences/A000118)

    Now consider the following :
    S(N) = Sigma [k=1,...,N] A(k)/k

    When N grows , S(N) grows closer to N*PI^2
    Now consider L(N) = S(N)- N*PI^2

    From a little model I built on Excel, It looks like
    L(N) = K + sum of periodic functions, where K = -0,6102

    Can someone help me with finding an expression for K and finding if the spectrum of L(N) is, as I suspect, connected with the Riemann zeta zeros.

    Thank you
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Sum of 4 squares and Riemann zeros
  1. Sums of Squares (Replies: 10)

  2. Sum of squares (Replies: 4)

  3. Riemann Zeta zeros (Replies: 31)

  4. Sum of squares? (Replies: 1)

  5. Sums of Squares (Replies: 2)

Loading...