论文标题
Zagier排名NAHM问题的两个示例的身份
Identities on Zagier's rank two examples for Nahm's problem
论文作者
论文摘要
令$ r \ geq 1 $为正整数，$ a $ a $ a真正的正定对称$ r \ times r $矩阵，$ b $ length $ r $的矢量和$ c $ scalar。 NAHM的问题是描述所有此类$ a，b $和$ c $带有理性条目，其中特定的$ r $ fold $ q $ q $ - hyperemetric系列（由$ f_ {a，b，c}（a，b，c}（q）$）涉及涉及参数$ a，b，c $的参数。当等级$ r = 2 $时，Zagier提供了11套$（a，b，c）$的示例，$ f_ {a，b，c}（q）$可能是模块化的。我们介绍了许多罗杰斯（Ragers） - 涉及双重和的ramanujan类型身份，为Zagier等级的两个示例提供了模块化表示。与文献中的几个已知案例一起，我们验证了Zagier的十个例子，并为其余的例子提供了猜想的身份。
Let $r\geq 1$ be a positive integer, $A$ a real positive definite symmetric $r\times r$ matrix, $B$ a vector of length $r$, and $C$ a scalar. Nahm's problem is to describe all such $A,B$ and $C$ with rational entries for which a specific $r$-fold $q$-hypergeometric series (denoted by $f_{A,B,C}(q)$) involving the parameters $A,B,C$ is modular. When the rank $r=2$, Zagier provided eleven sets of examples of $(A,B,C)$ for which $f_{A,B,C}(q)$ is likely to be modular. We present a number of Rogers--Ramanujan type identities involving double sums, which give modular representations for Zagier's rank two examples. Together with several known cases in the literature, we verified ten of Zagier's examples and give conjectural identities for the remaining example.
