Cohomological relation between Jacobi forms and skew‐holomorphic Jacobi forms |
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Authors: | Dohoon Choi Subong Lim |
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Affiliation: | 1. School of Liberal Arts and Sciences, Korea Aerospace University, Goyang, Gyeonggi, Republic of Korea;2. School of Mathematics, Korea Institute for Advanced Study, Dongdaemun‐gu, Seoul, Republic of Korea |
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Abstract: | Eichler and Zagier developed a theory of Jacobi forms to understand and extend Maass' work on the Saito‐Kurokawa conjecture. Later Skoruppa introduced skew‐holomorphic Jacobi forms, which play an important role in understanding liftings of modular forms and Jacobi forms. In this paper, we explain a relation between Jacobi forms and skew‐holomorphic Jacobi forms in terms of a group cohomology. More precisely, we introduce an isomorphism from the direct sum of the space of Jacobi cusp forms on and the space of skew‐holomorphic Jacobi cusp forms on with the same half‐integral weight to the Eichler cohomology group of with a coefficient module coming from polynomials. |
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Keywords: | Jacobi form Eichler cohomology 11F50 11F67 |
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