ON WIMAN BOUND FOR ARITHMETIC RIEMANN SURFACES
Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 173-177
Voir la notice de l'article provenant de la source Cambridge University Press
We show that the order of an automorphism of an arithmetic Riemann surface of genus $g$ is not greater than $2g\,{-}\,2$, provided $g$ is large enough. This bound is an arithmetic analog of the classical Wiman bound. We prove that it is sharp and attained for any genus but in contrast to the general case the automorphisms of maximal order act without fixed points. This allows us to consider the automorphisms which act on arithmetic Riemann surfaces and have a given number of fixed points. For these automorphisms we describe the asymptotic behavior of their orders.
BELOLIPETSKY, MIKHAIL; GROMADZKI, GRZEGORZ. ON WIMAN BOUND FOR ARITHMETIC RIEMANN SURFACES. Glasgow mathematical journal, Tome 45 (2003) no. 1, pp. 173-177. doi: 10.1017/S0017089502001131
@article{10_1017_S0017089502001131,
author = {BELOLIPETSKY, MIKHAIL and GROMADZKI, GRZEGORZ},
title = {ON {WIMAN} {BOUND} {FOR} {ARITHMETIC} {RIEMANN} {SURFACES}},
journal = {Glasgow mathematical journal},
pages = {173--177},
year = {2003},
volume = {45},
number = {1},
doi = {10.1017/S0017089502001131},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502001131/}
}
TY - JOUR AU - BELOLIPETSKY, MIKHAIL AU - GROMADZKI, GRZEGORZ TI - ON WIMAN BOUND FOR ARITHMETIC RIEMANN SURFACES JO - Glasgow mathematical journal PY - 2003 SP - 173 EP - 177 VL - 45 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089502001131/ DO - 10.1017/S0017089502001131 ID - 10_1017_S0017089502001131 ER -
%0 Journal Article %A BELOLIPETSKY, MIKHAIL %A GROMADZKI, GRZEGORZ %T ON WIMAN BOUND FOR ARITHMETIC RIEMANN SURFACES %J Glasgow mathematical journal %D 2003 %P 173-177 %V 45 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089502001131/ %R 10.1017/S0017089502001131 %F 10_1017_S0017089502001131
Cité par Sources :