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<p>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 group.</p>

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Symplectic Eichler criterion

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Shouhei Ma

摘要

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 group.