Trivial zeros of an L-function (awaiting review)

The zeros of an L-function $L(s)$ that occur at poles of its gamma factors are trivial zeros.

The presence of trivial zeros is required by the functional equation. In its analytic normalization, the L-function $L(s)$ has no zeros or poles in the right half-plane $\Re(s)>1$, but the gamma factors that appear in the functional equation have poles. Since the completed L-function has no poles (except possibly from Riemann zeta-function factors), the L-function must have zeros at poles of the gamma factors.

For arithmetic L-functions, the poles are at certain negative integers.