B-functions and holonomic systems. Rationality of roots of B-functions

DOI10.1007/BF01390168zbMath0354.35082OpenAlexW2883466814MaRDI QIDQ1236726

Publication date: 1976

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142441

Mathematics Subject Classification ID

Pseudodifferential operators and other generalizations of partial differential operators (35S99)

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Cites Work