四元二次型一类旋量的分类
Classification of one-class spinor genera for quaternary quadratic forms
摘要：
一个二次型有一个单类旋量亏格，如果它的旋量亏格由一个等价类组成。本文确定了只有一个原始四元亏格具有单类旋量亏格而不是单类亏格。在所有其他情况下，原始四元格的亏格要么有一个亏格和旋量亏格重合，要么亏格分裂成多个旋量亏格，而旋量亏格又分裂成多个等价类。
英文摘要：
A quadratic form has a one-class spinor genus if its spinor genus consists of a single equivalence class. In this paper, we determine that there is only one primitive quaternary genus which has a one-class spinor genus but not a one-class genus. In all other cases, the genera of primitive quaternary lattices either have a genus and spinor genus which coincide, or the the genus splits into multiple spinor genera, which in turn split into multiple equivalence classes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
