Symplectic Eichler criterion

Shouhei Ma

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arXiv · 2508.12624

Symplectic Eichler criterion

Shouhei Ma

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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.

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Shouhei Ma. 2025-08-18. Symplectic Eichler criterion. https://arxiv.org/abs/2508.12624

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