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ON THE EXISTENCE OF VECTOR-VALUED AUTOMORPHIC FORMS

2017
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Kyushu Journal of Mathematics
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While vector-valued automorphic forms can be defined for an arbitrary Fuchsian group and an arbitrary representation R of in GL(n, C), their existence, as far as we know, has been established in the literature only when restrictions are imposed on or R. In this paper, we prove the existence of n linearly independent vector-valued automorphic forms for any Fuchsian group and any n-dimensional complex representation R of . To this end, we realize these automorphic forms as global sections of a

doi:10.2206/kyushujm.71.271
fatcat:jeihpdd56rb45hmhreohl3rzdq