Geodesic
Difference Equation for Quintic $3$-Fold
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we use the Mellin–Barnes–Watson method to relate solutions of a certain type of $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; the first is the $q$-difference equation of $K$-theoretic $I$-function of the quintic, which is degree $25$; we use Adams' method to find the extra $20$ solutions at $Q=0$. The second special case is a fuchsian case, which is confluent to the differential equation of the cohomological $I$-function of the quintic. We compute the connection matrix and study the confluence of the $q$-difference structure.
Keywords: $q$-difference equation, quantum $K$-theory, Fermat quintic. 
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     author = {Yaoxinog Wen},
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Yaoxinog Wen. Difference Equation for Quintic $3$-Fold. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a42/

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