Introduction to Analytic Number Theory
《Introduction to Analytic Number Theory》 · 第 259 页 · Section 12.8「The functional equation for the Riemann zeta function」
Taking $s=2n+1$ in the functional equation, where $n=1,2,3,\ldots$, the factor $\cos(\pi s/2)$ vanishes and we find the so-called trivial zeros of $\zeta(s)$, $\zeta(-2n)=0$ for $n=1,2,3,\ldots$.