Zeta functions of alternate mirror Calabi–Yau families
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Peer-reviewed
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Article
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Abstract
We prove that if two Calabi-Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common factor is related to a hypergeometric Picard–Fuchs differential equation. The factor in the zeta function is defined over the rationals and has degree at least the order of the Picard–Fuchs equation. As an application, we relate several pencils of K3 surfaces to the Dwork pencil, obtaining new cases of arithmetic mirror symmetry.
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4904 Pure Mathematics, 49 Mathematical Sciences
Journal Title
Israel Journal of Mathematics
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Journal ISSN
0021-2172
1565-8511
1565-8511
Volume Title
228
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Springer Science and Business Media LLC
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Engineering and Physical Sciences Research Council (EP/N004922/1)