Abstract
We propose a deterministic primality test based on a section of a group scheme. Pépin's test and the tests of Lucas-Lehmer type are special cases of our construction, provided the group scheme is taken to be the multiplicative group and the Waterhouse-Weisfeiler group scheme, respectively. Besides, we suggest a test involving formal completions of these schemes.
Original language | English |
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Pages (from-to) | 555-564 |
Number of pages | 10 |
Journal | Archiv der Mathematik |
Volume | 93 |
Issue number | 6 |
DOIs | |
State | Published - Dec 2009 |
Bibliographical note
Funding Information:Acknowledgements. The authors’ research was supported in part by the Ministry of Absorption (Israel), the Minerva Foundation through the Emmy Noether Research Institute of Mathematics, and a grant from the Ministry of Science, Culture and Sport (Israel) and the Russian Foundation for Basic Research (the Russian Federation). A part of the work was done during the visit of the second named author to ENS (Paris) in April–May 2008. The support of these institutions is highly appreciated. We thank the referee for helpful suggestions.
Funding
Acknowledgements. The authors’ research was supported in part by the Ministry of Absorption (Israel), the Minerva Foundation through the Emmy Noether Research Institute of Mathematics, and a grant from the Ministry of Science, Culture and Sport (Israel) and the Russian Foundation for Basic Research (the Russian Federation). A part of the work was done during the visit of the second named author to ENS (Paris) in April–May 2008. The support of these institutions is highly appreciated. We thank the referee for helpful suggestions.
Funders | Funder number |
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Ministry of Absorption | |
Minerva Foundation | |
Russian Foundation for Basic Research | |
Ministry of Culture and Sport |
Keywords
- Formal group law
- Group scheme
- Primality testing