论文标题
双曲结的量子不变和三角产物的极端值
Quantum invariants of hyperbolic knots and extreme values of trigonometric products
论文作者
论文摘要
在本文中，我们研究函数$ j_ {4_1,0} $之间的关系，该函数源于图形结的量子不变，而Sudler的三角产品。我们发现$ j_ {4_1,0} $沿持续的分数收敛到二次非理性的不变因素，我们表明其渐近学偏离了Bettin和Drappeau在大型分数的情况下发现的普遍限制行为。我们将$ J_ {4_1,0} $的价值与Sudler的三角产品的价值联系起来，并为此为卢宾斯基的问题建立了此类Sudler产品的渐近上限和下限。
In this paper we study the relation between the function $J_{4_1,0}$, which arises from a quantum invariant of the figure-eight knot, and Sudler's trigonometric product. We find $J_{4_1,0}$ up to a constant factor along continued fraction convergents to a quadratic irrational, and we show that its asymptotics deviates from the universal limiting behavior that has been found by Bettin and Drappeau in the case of large partial quotients. We relate the value of $J_{4_1,0}$ to that of Sudler's trigonometric product, and establish asymptotic upper and lower bounds for such Sudler products in response to a question of Lubinsky.
