Displaying similar documents to “Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)”

Complex Hyperbolic Surfaces of Abelian Type

Holzapfel, R. (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07. We call a complex (quasiprojective) surface of hyperbolic type, iff – after removing finitely many points and/or curves – the universal cover is the complex two-dimensional unit ball. We characterize abelian surfaces which have a birational transform of hyperbolic type by the existence of a reduced divisor with only elliptic curve components and maximal singularity rate (equal to 4). We discover a...

Modular parametrizations of certain elliptic curves

Matija Kazalicki, Koji Tasaka (2014)

Acta Arithmetica

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Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings. ...