On Birch–Swinnerton-Dyer volumes for hypergeometric Calabi-Yau motives

Contact: Pieter Moree (moree@mpim-bonn.mpg.de)

We study the arithmetic of rank 4 weight 3 Calabi--Yau
motives in the framework of a broader program that approaches
regulators via differential equations that control them. We
introduce biextension periods for certain hypergeometric
CY motives and compare them numerically to the first derivative
of their $L$--functions at $s=2$, obtaining evidence in favor
of a B-SD-type conjecture.