On L-derivatives and biextensions of Calabi–Yau motives
We prove that certain differential operators of the form $ DLD $ with $ L $ hypergeometric and $ D=z\frac{\partial }{dz} $ are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Experimental Results |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2516712X23000151/type/journal_article |
| Summary: | We prove that certain differential operators of the form
$ DLD $
with
$ L $
hypergeometric and
$ D=z\frac{\partial }{dz} $
are of Picard–Fuchs type. We give closed hypergeometric expressions for minors of the biextension period matrices that arise from certain rank 4 weight 3 Calabi–Yau motives presumed to be of analytic rank 1. We compare their values numerically to the first derivative of the
$ L $
-functions of the respective motives at
$ s=2 $
. |
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| ISSN: | 2516-712X |