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Hypergeometric decomposition of symmetric K3 quartic pencils.

Authors :
Doran CF
Kelly TL
Salerno A
Sperber S
Voight J
Whitcher U
Source :
Research in the mathematical sciences [Res Math Sci] 2020; Vol. 7 (2), pp. 7. Date of Electronic Publication: 2020 Mar 16.
Publication Year :
2020

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.<br /> (© The Author(s) 2020.)

Details

Language :
English
ISSN :
2197-9847
Volume :
7
Issue :
2
Database :
MEDLINE
Journal :
Research in the mathematical sciences
Publication Type :
Academic Journal
Accession number :
32382704
Full Text :
https://doi.org/10.1007/s40687-020-0203-3