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Piateskii-Shapiro defined local $L$-factors $L^{PS}(s,\Pi,\Lambda)$ attachedto irreducible admissible representations $\Pi$ of the group $GSp(4)$ overlocal fields and Bessel models of $\Pi$ attached to Bessel data $\Lambda$.These local $L$-factors decompose into a product $L^{PS}(s,\Pi,\Lambda)=L^{PS}_{ex}(s,\Pi,\Lambda) L^{PS}_{reg}(s,\Pi,\Lambda)$ of an exceptional and aregular $L$-factor. In this paper we compute the exceptional factors$L^{PS}_{ex}(s,\Pi,\Lambda)$ for split Bessel models of $\Pi$.

Exceptional poles of local $L$-functions for $GSp(4)$ with respect to split Bessel models