HASSE-WEIL ZETA FUNCTION OF ABSOLUTELY IRREDUCIBLE SL2-REPRESENTATIONS OF THE FIGURE 8 KNOT GROUP

被引：3

作者：

Harada, Shinya ^{[1
]}

机构：

[1] KIAS, Sch Math, Seoul 130722, South Korea

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 09期

关键词：

Hasse-Weil zeta function; modular representation; topological invariant; figure; 8; knot; ELLIPTIC-CURVES; REPRESENTATIONS; VARIETIES;

D O I：

10.1090/S0002-9939-2011-10743-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Weil-type zeta functions defined by the numbers of absolutely irreducible SL2-representations of the figure 8 knot group over finite fields are computed explicitly. They are expressed in terms of the congruence zeta functions of reductions of a certain elliptic curve defined over the rational number field. Then the Hasse-Weil type zeta function of the figure 8 knot group is also studied. Its central value is written in terms of the Mahler measures of the Alexander polynomial of the figure 8 knot and a certain family of elliptic curves.

引用

页码：3115 / 3125

页数：11

共 22 条

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[2]

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