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A generalization of the reciprocity law of multiple Dedekind sums

Masahiro Asano (2007)

Annales de l’institut Fourier

Various multiple Dedekind sums were introduced by B.C.Berndt, L.Carlitz, S.Egami, D.Zagier and A.Bayad.In this paper, noticing the Jacobi form in Bayad [4], the cotangent function in Zagier [23], Egami’s result on cotangent functions [14] and their reciprocity laws, we study a special case of the Jacobi forms in Bayad [4] and deduce a generalization of Egami’s result on cotangent functions and a generalization of Zagier’s result. Further, we consider their reciprocity laws.

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

Grzegorz Kapustka, Michał Kapustka (2007)

Annales Polonici Mathematici

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.

New examples of modular rigid Calabi-Yau threefolds.

Matthias Schütt (2004)

Collectanea Mathematica

The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.

Quasimodular forms and quasimodular polynomials

Min Ho Lee (2012)

Annales mathématiques Blaise Pascal

This paper is based on lectures delivered at the Workshop on quasimodular forms held in June, 2010 in Besse, France, and it provides a survey of some recent work on quasimodular forms.

Quasi-modular forms attached to elliptic curves, I

Hossein Movasati (2012)

Annales mathématiques Blaise Pascal

In the present text we give a geometric interpretation of quasi-modular forms using moduli of elliptic curves with marked elements in their de Rham cohomologies. In this way differential equations of modular and quasi-modular forms are interpreted as vector fields on such moduli spaces and they can be calculated from the Gauss-Manin connection of the corresponding universal family of elliptic curves. For the full modular group such a differential equation is calculated and it turns out to be the...

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