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Sum of 4 squares and Riemann zeros

  1. Feb 9, 2007 #1

    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 [Broken])

    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
    Last edited by a moderator: May 2, 2017
  2. jcsd
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