We introduce a higher dimensional Atkin-Lehner theory for Siegel-Parahoric congruence subgroups of $GSp(2g)$. Old Siegel forms are induced by geometric correspondences on Siegel moduli spaces which commute with almost all local Hecke algebras. We also introduce an algorithm to get equations for moduli spaces of Siegel-Parahoric level structures, once we have equations for prime levels and square prime levels over the level one Siegel space. This way we give equations for an infinite tower of Siegel spaces after N. Elkies who did the genus one case.
Rastegar, A. (2017). On Atkin-Lehner correspondences on Siegel spaces. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 337-359.
MLA
Rastegar, A. "On Atkin-Lehner correspondences on Siegel spaces", Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 337-359.
HARVARD
Rastegar A. (2017). 'On Atkin-Lehner correspondences on Siegel spaces', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 337-359.
CHICAGO
A. Rastegar, "On Atkin-Lehner correspondences on Siegel spaces," Bulletin of the Iranian Mathematical Society, 43 Issue 4 (Special Issue) (2017): 337-359,
VANCOUVER
Rastegar A. On Atkin-Lehner correspondences on Siegel spaces. BIMS. 2017;43(Issue 4 (Special Issue)):337-359.
