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Exploring modular forms and the cohomology of local systems on moduli spaces by counting points. (English) Zbl 1446.11122
Ji, Lizhen (ed.) et al., Uniformization, Riemann-Hilbert correspondence, Calabi-Yau manifolds and Picard-Fuchs equations. Based on the conference, Institute Mittag-Leffler, Stockholm, Sweden, July 13–18, 2015. Somerville, MA: International Press; Beijing: Higher Education Press. Adv. Lect. Math. (ALM) 42, 81-109 (2018).
Summary: This is a report on a joint project in experimental mathematics with Jonas Bergström and Carel Faber where we obtain information about modular forms by counting curves over finite fields.
For the entire collection see [Zbl 1398.14003].
MSC:
11G20 Curves over finite and local fields
11F03 Modular and automorphic functions
14Q05 Computational aspects of algebraic curves
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