Geodesic
The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group
Amir Džambic1 ; Kristian Holm1 ; Ralf Köhl1
1Dept. of Mathematics, Christian-Albrechts-Universität, Kiel, Germany
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 527-556

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $n \geqslant 2$. We prove that, up to conjugation, SP$_{2n}$({\bf Z}) is the unique lattice in SP$_{2n}$({\bf R}) of the smallest covolume.
Classification : 22E40, 11E57, 20G30, 51M25
Mots-clés : Symplectic group, arithmetic group, lattice, covolume, Prasad's volume formula

Amir Džambic  1   ; Kristian Holm  1   ; Ralf Köhl  1

1 Dept. of Mathematics, Christian-Albrechts-Universität, Kiel, Germany 
Amir Džambic; Kristian Holm; Ralf Köhl. The Siegel Modular Group is the Lattice of Minimal Covolume in the Symplectic Group. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 527-556. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a3/
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     author = {Amir Džambic and Kristian Holm and Ralf K\"ohl},
     title = {The {Siegel} {Modular} {Group} is the {Lattice} of {Minimal} {Covolume} in the {Symplectic} {Group}},
     journal = {Journal of Lie Theory},
     pages = {527--556},
     year = {2025},
     volume = {35},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a3/}
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