Mathematics – Number Theory
Scientific paper
2009-07-15
Duke Math. J. 151 (2010), 175-218
Mathematics
Number Theory
36 pages, AmS-LaTeX; to appear in Duke Math. J. This is the first part of an originally larger paper arXiv:0709.1432, of the s
Scientific paper
We show that the Taylor coefficients of the series ${\bf q}(z)=z\exp({\bf G}(z)/{\bf F}(z))$ are integers, where ${\bf F}(z)$ and ${\bf G}(z)+\log(z) {\bf F}(z)$ are specific solutions of certain hypergeometric differential equations with maximal unipotent monodromy at $z=0$. We also address the question of finding the largest integer $u$ such that the Taylor coefficients of $(z ^{-1}{\bf q}(z))^{1/u}$ are still integers. As consequences, we are able to prove numerous integrality results for the Taylor coefficients of mirror maps of Calabi-Yau complete intersections in weighted projective spaces, which improve and refine previous results by Lian and Yau, and by Zudilin. In particular, we prove the general "integrality" conjecture of Zudilin about these mirror maps.
Krattenthaler Christian
Rivoal Tanguy
No associations
LandOfFree
On the integrality of the Taylor coefficients of mirror maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On the integrality of the Taylor coefficients of mirror maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the integrality of the Taylor coefficients of mirror maps will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-364529