Erratum to

Grzegorz Kapustka; Michał Kapustka

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Displaying similar documents to “Erratum to 'Modularity of a nonrigid Calabi-Yau manifold with bad reduction at 13' (Ann. Polon. Math. 90 (2007), 89-98)”

Modularity of a nonrigid Calabi-Yau manifold with bad reduction at 13

Grzegorz Kapustka, Michał Kapustka (2007)

Annales Polonici Mathematici

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We identify the weight four newform of a modular Calabi-Yau manifold studied by Hulek and Verrill. The main obstacle is that this Calabi-Yau manifold is not rigid and has bad reduction at prime 13. Replacing the original fiber product of elliptic fibrations with a fiberwise Kummer construction we reduce the problem to studying the modularity of a rigid Calabi-Yau manifold with good reduction at primes p ≥ 5.

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D. Choi (2006)

Acta Arithmetica

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Özlem Imamoglu, Yves Martin (2006)

Acta Arithmetica

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Acta Arithmetica

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Yichao Zhang (2011)

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Heima Hayashi (2006)

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Tate conjecture for twisted Siegel modular threefolds

Cristian Virdol (2011)

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Nonvanishing theorems for L-functions of modular forms and their derivatives.

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Inventiones mathematicae

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Modular equations for some η-products

(2013)

Acta Arithmetica

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The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.