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Linear relations for certain modular forms

โœ Scribed by J. H. van Lint


Publisher
John Wiley and Sons
Year
1959
Tongue
English
Weight
187 KB
Volume
20
Category
Article
ISSN
0025-584X

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We confirm a conjecture of L. Merel (H. Darmon and L. Merel, J. Reine Angew. Math. 490 (1997), 81-100) describing a certain relation between the jacobians of various quotients of X p in terms of specific correspondences. The method of proof involves reducing this conjecture to a question about certa

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## Abstract In this paper we study linear fractional relations defined in the following way. Let โ„‹๏ธ~__i__~ and โ„‹๏ธ~__i__~ ^โ€ฒ^, __i__ = 1, 2, be Hilbert spaces. We denote the space of bounded linear operators acting from โ„‹๏ธ~__j__~ to โ„‹๏ธ~__i__~ ^โ€ฒ^ by __L__ (โ„‹๏ธ~__j__~ , โ„‹๏ธ~__i__~ ^โ€ฒ^). Let __T__ โˆˆ

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Let G be a connected semisimple Lie group with finite center, and suppose G contains a compact Cartan subgroup T. Certain irreducible unitary representations of G arise as spaces of harmonic forms associated to Dolbeault cohomology of line bundles over the complex homogeneous space Gร‚T. In this work