A counterexample in the theory of local zeta functions
Martin, Roland
Experiment. Math., Tome 4 (1995) no. 4, p. 299-305 / Harvested from Project Euclid
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The generalized Igusa local zeta function $Z_{\Q _p}(s)$ associated to $(\SL_7,\rho)$, where $\rho$ is the Cartan product of the first, third and fifth fundamental representations of $\SL_7$, is explicitly computed and shown not to satisfy the expected functional equation $$Z_{\Q _p}(s)|_{p \mapsto p^{-1}}=p^{-7s}Z_{\Q _p}(s).$$
Publié le : 1995-05-14
Classification:  11S40 
@article{1047674390,
     author = {Martin, Roland},
     title = {A counterexample in the theory of local zeta functions},
     journal = {Experiment. Math.},
     volume = {4},
     number = {4},
     year = {1995},
     pages = { 299-305},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047674390}
}

Martin, Roland. A counterexample in the theory of local zeta functions. Experiment. Math., Tome 4 (1995) no. 4, pp.  299-305. http://gdmltest.u-ga.fr/item/1047674390/