English

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}
}
R2 v1 2026-07-01T04:54:13.644Z