整体函数域上不可分二次格的构作

王瑞卿

数学学报 ›› 2016, Vol. 59 ›› Issue (3) : 295-302.

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PDF(410 KB)
数学学报 ›› 2016, Vol. 59 ›› Issue (3) : 295-302. DOI: 10.12386/A2016sxxb0027
论文

整体函数域上不可分二次格的构作

    王瑞卿
作者信息 +

The Construction of Indecomposable Quadratic Lattices over Global Function Fields

    Rui Qing WANG
Author information +
文章历史 +

摘要

构作了有理函数域F19(x)上秩3到6的不可分格,回答了Gerstein关于整体函数域上是否存在秩5的不可分格的问题.

Abstract

We construct indecomposable quadratic lattices of rank 3,4,5 and 6 over a suitable Hasse domain of the rational function field F19(x),which,in particular,solves the problem proposed by Gerstein about the existence of indecomposable quadratic lattices of rank 5 over global function fields.

关键词

不可分格 / 整体函数域 / Hasse环 / 约当分裂 / 类数

Key words

indecomposable lattice / global function field / Hasse domain / Jordan splitting / class number

引用本文

导出引用
王瑞卿. 整体函数域上不可分二次格的构作. 数学学报, 2016, 59(3): 295-302 https://doi.org/10.12386/A2016sxxb0027
Rui Qing WANG. The Construction of Indecomposable Quadratic Lattices over Global Function Fields. Acta Mathematica Sinica, Chinese Series, 2016, 59(3): 295-302 https://doi.org/10.12386/A2016sxxb0027

参考文献

[1] Benham J. W., Hsia J. S., Spinor equivalence of quadratic forms, J. Number Theory, 1983, 17:337-342.
[2] Gerstein L. J., Splitting quadratic forms over integers of global fields, Amer. J. Math., 1969, 91:106-134.
[3] Gerstein L. J., Unimodular quadratic forms over global function fields, J. Number Theory, 1979, 11:529-541.
[4] Gerstein L. J., A note on splitting quadratic forms, J. Number Theory, 1988, 29:231-233.
[5] Gerstein L. J., Indecomposable integral quadratic forms over global function fields, Acta Arith., 2000, 96:89-95.
[6] Gerstein L. J., Basic Quadratic Forms, Graduate Studies in Mathematics 90, Amer. Math. Soc., Providence, 2008.
[7] O'Meara O. T., Introduction to Quadratic Forms, Springer-Verlag, Berlin, New York, 1973.
[8] O'Meara O. T., The construction of indecomposable positive definite quadratic forms, J. Reine Angew. Math., 1975, 276:99-123.
[9] Rosen M., Number Theory in Function Fields, Springer-Verlag, New York, Berlin, Heidelberg, 2002.

基金

河南省基础与前沿研究计划资助项目(132300410373)

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