Number theory casting a look at the mirror

Details Number theory casting a look at the mirror Number theory casting a look at the mirror

2000-08-31

arxiv.org/abs/math/0008237v2

Mathematics

Number Theory

17 AmSTeX pages, 1 figure uses mfpic (added in source); to A.B.Shidlovskii on the occasion of his 85th birthday; submitted for

Scientific paper

In this work, we give a purely analytic introduction to the phenomenon of mirror symmetry for quintic threefolds via classical hypergeometric functions and differential equations for them. Starting with a modular map and recent transcendence results for its values, we regard a mirror map $z(q)$ as a concept generalizing the modular one. We give an alternative approach demonstrating the existence of non-linear differential equations for the mirror map, and exploit both an elegant construction of Klemm-Lian-Roan-Yau and the Ax theorem to prove that the Yukawa coupling $K(q)$ does not satisfy any algebraic differential equation of order less than 7 with coefficients from $\mathbb{C}(q)$.

Affiliated with

Also associated with

No associations

Rating

Number theory casting a look at the mirror 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 Number theory casting a look at the mirror, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Number theory casting a look at the mirror will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-268335