Symplectic Eichler criterion
Number Theory
2025-08-19 v1 Algebraic Geometry
Abstract
We prove an Eichler-type criterion for symplectic lattices which determines in a simple way when two primitive vectors are equivalent under a canonical congruence subgroup of the symplectic group. This is supplemented by another, related criterion which determines when a given primitive vector is splitting. Both criteria use the discriminant groups.
Keywords
Cite
@article{arxiv.2508.12624,
title = {Symplectic Eichler criterion},
author = {Shouhei Ma},
journal= {arXiv preprint arXiv:2508.12624},
year = {2025}
}