The sum of like powers of the zeros of the Riemann zeta function
The sum of like powers of the zeros of the Riemann zeta function
In this paper we discuss a method of evaluating the sum <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma Subscript r Baseline equals sigma-summation rho Superscript negative r"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>σ<!-- σ --></mml:mi> <mml:mi>r</mml:mi> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mo>∑<!-- ∑ --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>ρ<!-- ρ --></mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> …