Affiliation:
1. School of Mathematical Sciences , Shanghai Jiao Tong University , Shanghai , P. R. China
Abstract
Abstract
We express the Mahler measures of 23 families of Laurent polynomials in terms of Eisenstein–Kronecker series.
These Laurent polynomials arise as Landau–Ginzburg potentials on Fano 3-folds,
sixteen of which define
K
3
{K3}
hypersurfaces of generic Picard rank 19, and the rest are of generic Picard rank less than 19.
We relate the Mahler measure at each rational singular moduli to the value at 3 of the L-function of some weight-3 newform.
Moreover, we find ten exotic relations among the Mahler measures of these families.
Subject
Applied Mathematics,General Mathematics
Reference37 articles.
1. S. Ahlgren, K. Ono and D. Penniston,
Zeta functions of an infinite family of K3{K3} surfaces,
Amer. J. Math. 124 (2002), no. 2, 353–368.
2. M. Akhtar, T. Coates, S. Galkin and A. M. Kasprzyk,
Minkowski polynomials and mutations,
SIGMA Symmetry Integrability Geom. Methods Appl. 8 (2012), Paper No. 094.
3. V. V. Batyrev,
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties,
J. Algebraic Geom. 3 (1994), no. 3, 493–535.
4. M.-J. Bertin,
Mesure de Mahler d’une famille de polynômes,
J. Reine Angew. Math. 569 (2004), 175–188.
5. M.-J. Bertin,
Mesure de Mahler d’hypersurfaces K3{K3},
J. Number Theory 128 (2008), no. 11, 2890–2913.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献