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cmr10JulyUU23,2003. !Ksrc:44lfunktio.tex2t: cmbx9Abstractэ 1o cmr9Inthey9ear1923EmilArtinin9troAducedhisnew35" cmmi9L-functionsbAelongingto Galois c9haracters.EButhis theorywasstillincompleteintworespAects. First,thetheorydepAendedonthev|ralidit9yoftheGeneralReciproAcit9yLaw whic9hArtinwasunableatthattimetoproveinfullgenerality:.PSecondly, intheexplicitdenitionofL-functionstheramiedprimescouldnot bAeP)tak9enintoaccount;mhencethatdenitionwasofprovisionalcharacter onlyzwhereastheznaldenitioncouldbAegiv9eninaratherindirectw9ay only:.Inlatery9earsArtinlledbAothofthesegaps:
In1927heprovedthe General