# Sum of 4 squares and Riemann zeros

1. Feb 9, 2007

### chrisina

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 [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