The Hurwitz quaternion order is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann surface theory, in connection with surfaces with maximal symmetry, namely the Hurwitz surfaces.[1] The Hurwitz quaternion order was studied in 1967 by Goro Shimura,[2] but first explicitly described by Noam Elkies in 1998.[3] For an alternative use of the term, see Hurwitz quaternion (both usages are current in the literature).
^Vogeler, Roger (2003), On the geometry of Hurwitz surfaces (PhD), Florida State University.
^Shimura, Goro (1967), "Construction of class fields and zeta functions of algebraic curves", Annals of Mathematics, Second Series, 85 (1): 58–159, doi:10.2307/1970526, JSTOR 1970526, MR 0204426.
^Elkies, Noam D. (1998), "Shimura curve computations", Algorithmic number theory (Portland, OR, 1998), Lecture Notes in Computer Science, vol. 1423, Berlin: Springer-Verlag, pp. 1–47, arXiv:math.NT/0005160, doi:10.1007/BFb0054850, MR 1726059.
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The Hurwitzquaternionorder is a specific order in a quaternion algebra over a suitable number field. The order is of particular importance in Riemann...
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advanced the study of the Hurwitz problem with a survey of efforts to that date, and by exhibiting the method of doubling the quaternions to obtain Cayley numbers...
maximal order of D {\displaystyle D} (see Hurwitzquaternionorder), described explicitly by Noam Elkies [1]. In order to construct the first Hurwitz triplet...
_{g})\geq {\frac {4}{3}}\log g,} resulting from an analysis of the Hurwitzquaternionorder. A similar bound holds for more general arithmetic Fuchsian groups...
can be obtained as the surface associated to a particular order, the Hurwitzquaternionorder, and it is compact of volume π / 21 {\displaystyle \pi /21}...
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quaternions. The nonexistence of nontrivial vector-valued cross products of two vectors in other dimensions is related to the result from Hurwitz's theorem...
group of units of the Hurwitzquaternions, which has order 24, contains a normal subgroup of order 8 isomorphic to the quaternion group, and is the binary...
Theo Douvropoulos; Joel Brewster Lewis; Alejandro H. Morales (2022), "Hurwitz Numbers for Reflection Groups I: Generatingfunctionology", Enumerative...
article on quaternions and spatial rotations.) Explicitly, the binary tetrahedral group is given as the group of units in the ring of Hurwitz integers....
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