p-adic单位圆盘上q-括号的不动点
数论
2011-07-14 v2
摘要
我们研究了复单位圆盘上q-括号的不动点，并证明了以下结论。满足[x]_q=x的（非平凡）对(x,q)的集合构成一个流形，其标准投影的度数均为p-2。存在一个解析函数Q(X)，将x映射到满足[x]_q=x的q，该函数是一个（双射）压缩映射，除非在q上的纤维中x的余数的重数为2。该理论在Z_p上的限制是平凡的，除非p=3。
引用
@article{arxiv.0902.4284,
title = {Fixed Points of the q-Bracket on the p-Adic Unit Disk},
author = {Eric Brussel},
journal= {arXiv preprint arXiv:0902.4284},
year = {2011}
}
备注
11 pages. The new version (7/11) has an expanded introduction and some sharper results now contained in Theorem 6, including a criterion for when the map Q(X) is a contraction (the multiplicity of the residue of x should be 1). There is no more Proposition 7 and 8. There are also slight notation changes throughout, to enhance the exposition