Riemann zeta function

noun2

1. •
   The function ζ defined by the Dirichlet series ζ(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.

   • It is straightforward to show that the Riemann zeta function has zeros at the negative even integers and these are called the trivial zeros of the Riemann zeta function. — 2004
2. •
   A usage of (a specified value of) the Riemann zeta function, such as in an equation.

   • Page 203 is an isolated page on which Ramanujan evaluates six quotients of either Riemann zeta functions or L-functions. — 2013