Divisors, spin sums and the functional equation of the Zeta-Riemann function

Summary

Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>S_n$, $n=1,2\dots$ be the sequence of partial sums of independent spin random variables. We show that the distribution value of the divisors of $S_n$, is intimately related to the Zeta-Riemann function via the functional equation and Theta elliptic functions.