Bolza Quaternion Order and Asymptotics of Systoles Along Congruence Subgroups
| Autor: | Mikhail G. Katz, Uzi Vishne, Michael M. Schein, Karin U. Katz |
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| Rok vydání: | 2016 |
| Předmět: |
Mathematics - Differential Geometry
Fuchsian group Pure mathematics Quaternion algebra Mathematics::Number Theory General Mathematics 010102 general mathematics Mathematics - Rings and Algebras 01 natural sciences Ring of integers Differential Geometry (math.DG) Rings and Algebras (math.RA) 0103 physical sciences FOS: Mathematics 53C23 11R52 16K20 010307 mathematical physics 0101 mathematics Invariant (mathematics) Quaternion Triangle group Congruence subgroup Mathematics Bolza surface |
| Zdroj: | Experimental Mathematics. 25:399-415 |
| ISSN: | 1944-950X 1058-6458 |
| DOI: | 10.1080/10586458.2015.1073642 |
| Popis: | We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4/3 log g(X) on the systole, where g is the genus. We also exhibit the Bolza group as a congruence subgroup, and calculate out a few examples of "Bolza twins" (using magma). Like the Hurwitz triplets, these correspond to the factoring of certain rational primes in the ring of integers of the invariant trace field of the surface. We exploit random sampling combined with the Reidemeister-Schreier algorithm as implemented in magma to generate these surfaces. 35 pages, to appear in Experimental Mathematics |
| Databáze: | OpenAIRE |
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