Projects per year
Abstract
We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global $L$-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.
Original language | English |
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Article number | 7 |
Number of pages | 70 |
Journal | Research in the Mathematical Sciences |
Volume | 7 |
Issue number | 2 |
Early online date | 16 Mar 2020 |
DOIs | |
Publication status | E-pub ahead of print - 16 Mar 2020 |
ASJC Scopus subject areas
- Theoretical Computer Science
- Mathematics (miscellaneous)
- Computational Mathematics
- Applied Mathematics
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Dive into the research topics of 'Hypergeometric Decomposition of Symmetric K3 Quartic Pencils'. Together they form a unique fingerprint.Projects
- 1 Finished
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Bridging Frameworks via Mirror Symmetry
Engineering & Physical Science Research Council
1/09/18 → 31/08/19
Project: Research Councils