论文标题
奇异的双八八倍三倍和模块化形式的时期
Periods of singular double octic Calabi-Yau threefolds and modular forms
论文作者
论文摘要
根据模块化定理，每个刚性的calabi-yau三倍$ x $都具有相关的模块化表格$ f $，以使$ l $ functions $ l（x，s）= l（f，s）$ hold的平等性。在这种情况下，$ x $的积分预计将以特殊值$ l（f，1）$和$ l（f，2）$表示。我们建议对$ x $的节点模型的时期积分进行类似的解释。它是根据$ f $的梅林变换的某些变体给出的。我们基于双重八元案例提供了对这种解释的数值证据。
By the modularity theorem every rigid Calabi-Yau threefold $X$ has associated modular form $f$ such that the equality of $L$-functions $L(X,s)=L(f,s)$ holds. In this case period integrals of $X$ are expected to be expressible in terms of the special values $L(f,1)$ and $L(f,2)$. We propose a similar interpretation of period integrals of a nodal model of $X$. It is given in terms of certain variants of a Mellin transform of $f$. We provide numerical evidence towards this interpretation based on a case of double octics.
