On \(\mathrm{Sp}_4\) modularity of Picard-Fuchs differential equations for Calabi-Yau threefolds. (English) Zbl 1283.11073

Yang, Yifan; Zudilin, Wadim

Amdeberhan, Tewodros (ed.) et al., Gems in experimental mathematics. AMS special session on experimental mathematics, Washington, DC, January 5, 2009. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4869-2/pbk). Contemporary Mathematics 517, 381-413 (2010).

Summary: Motivated by the relationship of classical modular functions and Picard-Fuchs linear differential equations of order 2 and 3, we present an analogous concept for equations of order 4 and 5.
For the entire collection see [Zbl 1193.00060].

MSC:

11F23	Relations with algebraic geometry and topology
11F46	Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
14J32	Calabi-Yau manifolds (algebro-geometric aspects)
34M15	Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain
34M35	Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms