论文标题
沃斯基安代数和broadhurst-Roberts二次关系
Wrońskian algebra and Broadhurst-Roberts quadratic relations
论文作者
论文摘要
通过对贝塞尔时刻可缩小的条目的Wroxkian矩阵的代数操纵，我们提供了Broadhurst和Roberts猜想的二次关系的新分析证明，以及一些概括。在Wroxkian框架中，我们通过Vanhove的差分运算符中的多项式系数重新解释了DE RHAM相交的配对，并通过线性总和规则来计算Betti相交配对，以进行shell和Offshell Feynman图，并在Threshold Momenta时进行shell Feynman图。从Broadhurst-Roberts二次关系产生的理想中，我们得出了用于壳上Feynman图的新的非线性总和规则，包括一个无限的确定性身份家族，这些家族与deligne的关键价值兼容了动机$ L $ unctuctions的关键价值。
Through algebraic manipulations on Wrońskian matrices whose entries are reducible to Bessel moments, we present a new analytic proof of the quadratic relations conjectured by Broadhurst and Roberts, along with some generalizations. In the Wrońskian framework, we reinterpret the de Rham intersection pairing through polynomial coefficients in Vanhove's differential operators, and compute the Betti intersection pairing via linear sum rules for on-shell and off-shell Feynman diagrams at threshold momenta. From the ideal generated by Broadhurst--Roberts quadratic relations, we derive new non-linear sum rules for on-shell Feynman diagrams, including an infinite family of determinant identities that are compatible with Deligne's conjectures for critical values of motivic $L$-functions.
