Some new results on the Eichler cohomology of automorphic forms
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Publication:4043131
DOI10.1090/S0002-9904-1974-13520-2zbMath0292.10022MaRDI QIDQ4043131
Publication date: 1974
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Modular and automorphic functions (11F03) Automorphic forms, one variable (11F12) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)
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Cites Work
- Eine Verallgemeinerung der Abelschen Integrale
- On complementary automorphic forms and supplementary Fourier series
- A bounded automorphic form of dimension zero is constant
- On cohomology of Kleinian groups
- The Eichler cohomology of a Kleinian group
- Eichler cohomology and automorphic forms
- Zur analytischen Theorie der Grenzkreisgruppen. II. Divisorentheorie der automorphen Formen komplexer Dimension
- Invarianten linearer Differentialgleichungen
- Explizite Konstruktion der automorphen Orthogonalfunktionen in den multiplikativen Differentialklassen
- The Eichler Cohomology Groups and Automorphic Forms
- Grenzkreisgruppen und kettenbruchartige Algorithmen
- Notes on automorphic functions: an entire automorphic form of positive dimension is zero
- Automorphic integrals with preassigned periods
- Automorphe Formen als metrische Invarianten. Teil I: Automorphe Formen, metrische Verknüpfung, Eigenfunktionen linearer Funktionale
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