| 陶志雄.Jones多项式的零点[J].数学年刊A辑,2011,32(1):63~70 |
| Jones多项式的零点 |
| On the Zeros of Jones Polynomial |
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| DOI： |
| 中文关键词: 纽结 链环 Jones多项式 多项式的零点 Mahler测度 |
| 英文关键词:Knot Link Jones polynomial Zeros of polynomial Mahler measure |
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| 中文摘要: |
| 利用数论理论证明了纽结的Jones多项式仅有可能的有理根是O,而链环的Jones多项式仅有可能的有理根是0和-1.给出了作为Jones多项式根的所有可能单位根,以及所有可能的具有平凡Mahler测度的Jones多项式.最后指出了交叉数不超过11的纽结中,只有4_1,8_9,9_(42),K11n19的Jones多项式具有平凡的Mahler测度,从而回答了林晓松提出的关于Mahler测度的一个问题. |
| 英文摘要: |
| By using the number theory, this author proves that the only possible rational root of the Jones polynomial of a knot is $0$ and the only
possible rational roots of the Jones polynomial of a link are $0$ and $-1$. Both all the possible roots of unity which are zeros
of the Jones polynomials and all the possible Jones polynomials which have trivial Mahler measure are given. Finally, it
is indicated that in all knots with up to 11 crossings, only the Jones polynomials of $4_1, 8_9, 9_{42}, K11n19$ have trivial Mahler measure and
then it answers one of Lin's problems. |
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