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Given an induced representation of Langlands type    (  π  ,   V  π   )    ofGL  n    (  F  )with   F   non‐Archimedean, we show that there exist explicit choices of matrix coefficient   β   and Schwartz–Bruhat function   Φ   for which the Godement–Jacquet zeta integral    Z  (  s  ,  β  ,  Φ  )    attains the   L  ‐function    L  (  s  ,  π  )   .

Test vectors for non‐Archimedean Godement–Jacquet zeta integrals