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We study the local factor at p of the semi-simple zeta function of a Shimuravariety of Drinfeld type for a level structure given at p by the pro-unipotentradical of an Iwahori subgroup. Our method is an adaptation to this case of theLanglands-Kottwitz counting method. We use Hecke algebra isomorphisms todetermine the test functions at p.

Shimura varieties with $\Gamma_1(p)$-level via Hecke algebra isomorphisms: the Drinfeld case