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[]\OT1/cmr/m/n/10.95 When $\OML/cmm/m/it/10.95 g$ \OT1/cmr/m/n/10.95 is an Eise
n-stein se-ries, Propo-si-tion 1.3[] shows that the cus-p-i-dal gen-er-alised e
igenspace
 []

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[]\OT1/cmr/m/n/10.95 This hy-poth-e-sis im-plies that the signs which oc-cur in
 the func-tional equa-tions for $\OML/cmm/m/it/10.95 L\OT1/cmr/m/n/10.95 (\OML/
cmm/m/it/10.95 E; V[]; s\OT1/cmr/m/n/10.95 )$
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\OT1/cmr/m/n/10.95 (1\OML/cmm/m/it/10.95 ; \OT1/cmr/m/n/10.95 1)$, Katz's $\OML
/cmm/m/it/10.95 p$\OT1/cmr/m/n/10.95 -adic $\OML/cmm/m/it/10.95 L$\OT1/cmr/m/n/
10.95 -function sat-is-fies the func-tional equa-tion $\OML/cmm/m/it/10.95 L[]\
OT1/cmr/m/n/10.95 (\OML/cmm/m/it/10.95 K\OT1/cmr/m/n/10.95 )(\OML/cmm/m/it/10.9
5  \OT1/cmr/m/n/10.95 ) = \OML/cmm/m/it/10.95 L[]\OT1/cmr/m/n/10.95 (\OML/cmm/m
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OT1/cmr/bx/n/10.95 N[]\OT1/cmr/m/n/10.95 )$
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