Le théorème de Schanuel pour un corps non commutatif
Rendiconti del Seminario Matematico della Università di Padova, Volume 130 (2013), p. 221-282
@article{RSMUP_2013__130__221_0,
     author = {R\'emond, Ga\"el and Zehrt-Liebend\"orfer, Christine},
     title = {Le th\'eor\`eme de Schanuel pour un corps non commutatif},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {130},
     year = {2013},
     pages = {221-282},
     mrnumber = {3148640},
     language = {fr},
     url = {http://www.numdam.org/item/RSMUP_2013__130__221_0}
}
Rémond, Gaël; Zehrt-Liebendörfer, Christine. Le théorème de Schanuel pour un corps non commutatif. Rendiconti del Seminario Matematico della Università di Padova, Volume 130 (2013) pp. 221-282. http://www.numdam.org/item/RSMUP_2013__130__221_0/

[B] T. Borek, Arakelov theory of noncommutative arithmetic curves. J. Number Theory, 131 (2011), pp. 212-227. | MR 2736852 | Zbl 1213.14008

[Ca] J. W. S. Cassels, An introduction to the geometry of numbers. Springer, Berlin, 1959. | MR 157947

[Ch] H. Chaix, Démonstration élémentaire d'un théoréme de Van der Corput. C. R. A. S. 275 (1972), pp. 883-885. | MR 311608 | Zbl 0244.10025

[CG] C. Christensen - W. Gubler, Der relative Satz von Schanuel. Manuscripta Math, 126 (2008), pp. 505-525. | MR 2425438 | Zbl 1155.11034

[Da] H. Davenport, On a principle of Lipschitz. J. London Math. Soc. 26 (1951), pp. 179-183. | MR 43821 | Zbl 0042.27504

[De] M. Deuring, Algebren. Springer, Berlin, 1968. | MR 228526 | Zbl 0159.04201

[FMT] J. Franke - Y. Manin - Y. Tschinkel, Rational points of bounded height on Fano varieties. Invent. Math. 95 (1989), pp. 421-435. Erratum c;ibid. 102 (1990), p. 463. | MR 974910 | Zbl 0709.14017

[FP] D. Farenick - B. Pidkowich, The spectral theorem in quaternions. Lin. Alg. Appl. 371 (2003), pp. 75-102. | MR 1997364 | Zbl 1030.15015

[G] C. Gasbarri, On the number of points of bounded height on arithmetic projective spaces. Manuscripta Math. 98 (1999), pp. 453-475. | MR 1689992 | Zbl 0991.11036

[J] N. Jacobson, Basic Algebra I. Freeman, San Francisco, 1974. | MR 356989

[La] S. Lang, Algebraic number theory. Addison-Wesley, Reading, Mass. 1970. | MR 282947

[Le] A. Leutbecher, Zahlentheorie. Springer, Berlin, 1996.

[LR] C. Liebendörfer - G. Rémond, Hauteurs de sous-espaces sur les corps non commutatifs. Math. Z. 255 (2007), pp. 549-577. | MR 2270288

[MV] D. Masser - J. Vaaler, Counting algebraic numbers with large height II. Trans. Amer. Math. Soc. 359 (2007), pp. 427-445. | MR 2247898

[N] W. Narkiewicz, Elementary and analytic theory of algebraic numbers. Springer, Berlin, 1990. | MR 1055830

[P] E. Peyre, Hauteurs et mesures de Tamagawa sur les variétés de Fano. Duke Math. J. 79 (1995), pp. 101-218. | MR 1340296

[R] I. Reiner, Maximal orders. Academic Press, London, 1975. | MR 1972204

[Scha] S. H. Schanuel, Heights in number fields. Bull. Soc. Math. Fr. 107 (1979), pp. 433-449. | MR 557080

[Schm] W. Schmidt, The distribution of sublattices of m . Monatsh. Math. 125 (1998), pp. 37-81. | MR 1485976

[St] R. P. Stanley, Enumerative Combinatorics. Volume 1, Cambridge University Press, 1997. | MR 1442260

[T1] J. L. Thunder, An asymptotic estimate for heights of algebraic subspaces. Trans. Amer. Math. Soc. 331 (1992), pp. 395-424. | MR 1072102

[T2] J. L. Thunder, The number of solutions of bounded height to a system of linear equations. J. Number Theory. 43 (1993), pp. 228-250. | MR 1207503

[V] P. Voutier, An effective lower bound for the height of algebraic numbers. Acta Arithm. 74 (1996), pp. 81-95. | MR 1367580

[W] M. Widmer, Counting primitive points of bounded height. Trans. Amer. Math. Soc. 362 (2010), pp. 4793-4829. | MR 2645051