A geometrical approach to the theory of Jacobi forms
Jürg Kramer (1991)
Compositio Mathematica
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Jürg Kramer (1991)
Compositio Mathematica
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Skogman, Howard (2004)
International Journal of Mathematics and Mathematical Sciences
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Min Ho Lee (1998)
Collectanea Mathematica
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We generalize Jacobi forms of an arbitrary degree and construct torus bundles over abelian schemes whose sections can be identified with such generalized Jacobi forms.
Min Ho Lee (2015)
Acta Arithmetica
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Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular...
Rolf BERNDT, Siegfried Böcherer (1990)
Mathematische Zeitschrift
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Hidenori Katsurada, Hisa-aki Kawamura (2010)
Acta Arithmetica
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Mohammad Hailat (1991)
Fundamenta Mathematicae
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Rolf Berndt (1994)
Manuscripta mathematica
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Minking Eie (2000)
Revista Matemática Iberoamericana
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We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.
Nils-Peter Skoruppa (1991)
Journal de théorie des nombres de Bordeaux
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We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
Joachim Dulinski (1995)
Mathematische Annalen
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