Abstract
We discuss a number of examples of rigid Calabi-Yau varieties for which one can prove modularity. In this situation the number N p of F p -rational points of the Calabi-Yau is (via the Lefschetz fixed point formula) related to the Fourier coefficient a p of some modular form. In all cases which we discuss it turns out that it is much faster to compute a p than N p .
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Hulek, K., Spandaw, J. (2001). Counting Points on Calabi-Yau Threefolds. In: Ciliberto, C., Hirzebruch, F., Miranda, R., Teicher, M. (eds) Applications of Algebraic Geometry to Coding Theory, Physics and Computation. NATO Science Series, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1011-5_10
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DOI: https://doi.org/10.1007/978-94-010-1011-5_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0005-8
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