Orateur
Description
We identify the Frobenius numerators of the higher-Bessel multiplication kernel with MacMahon’s multiset Eulerian polynomials. This gives a combinatorial description of polynomial coefficients arising from period integrals. This identification explains why the polynomials appeared in the product kernels are palindromic, have simple negative zeros, and have positive integer coefficients. The descent refinement specializes to the Dwork period and a common Landau-Ginzburg potential relates this period to the higher-Bessel function. We also identify the Newton polytope of the kernel’s Laurent model as the polar of the type - $A_{N-1}$ root polytope and give a complete-intersection presentation in $(P1)^N$. For $N = 5$ this has the configuration occurring in mirror Hulek–Verrill geometry. These explicit and motivate links with the Calabi–Yau geometry of Feynman integrals.
Based on a joint paper with Ilya Gaiur, Feihu Liu and Zihao Zhang.