naa a22 4500 510782396 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s11856-012-0117-x doi (NATIONALLICENCE)springer-10.1007/s11856-012-0117-x Splitting fields of characteristic polynomials of random elements in arithmetic groups [Elektronische Daten] [F. Jouve, E. Kowalski, D. Zywina] We discuss rather systematically the principle, implicit in earlier works, that for a "random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the splitting field of the characteristic polynomial, computed using any faitfhful representation, has Galois group isomorphic to the Weyl group of the underlying algebraic group. Besides tools such as the large sieve, which we had already used, we introduce some probabilistic ideas (large deviation estimates for finite Markov chains) and the general case involves a more precise understanding of the way Frobenius conjugacy classes are computed for such splitting fields (which is related to a map between regular elements of a finite group of Lie type and conjugacy classes in the Weyl group which had been considered earlier by Carter and Fulman for other purposes; we show in particular that the values of this map are equidistributed). Hebrew University Magnes Press, 2012 Jouve F. Département de Mathématiques, Bâtiment 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405, Orsay Cedex, France aut Kowalski E. ETH Zürich — DMATH, Rämistrasse 101, 8092, Zürich, Switzerland aut Zywina D. Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, ON, Canada aut Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 263-307 0021-2172 193:1<263 2013 193 11856 https://doi.org/10.1007/s11856-012-0117-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-012-0117-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jouve F. Département de Mathématiques, Bâtiment 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405, Orsay Cedex, France aut NATIONALLICENCE 700 1- Kowalski E. ETH Zürich — DMATH, Rämistrasse 101, 8092, Zürich, Switzerland aut NATIONALLICENCE 700 1- Zywina D. Department of Mathematics and Statistics, Queen's University, K7L 3N6, Kingston, ON, Canada aut NATIONALLICENCE 773 0- Israel Journal of Mathematics The Hebrew University Magnes Press 193/1(2013-01-01), 263-307 0021-2172 193:1<263 2013 193 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer