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Mock modular forms and quantum modular forms
Proceedings of the American Mathematical Society, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Choi, Dohoon +2 more
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2008
Modular functions played a prominent role in the mathematics of the 19th century, where they appear in the theory of elliptic functions, i.e., elements of the function field of an elliptic curve, but also in the theory of binary quadratic forms. The term seems to stem from Dirichlet, but the functions are clearly present in the works of Gauss, Abel and
Edixhoven, B. +2 more
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Modular functions played a prominent role in the mathematics of the 19th century, where they appear in the theory of elliptic functions, i.e., elements of the function field of an elliptic curve, but also in the theory of binary quadratic forms. The term seems to stem from Dirichlet, but the functions are clearly present in the works of Gauss, Abel and
Edixhoven, B. +2 more
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Oberwolfach Reports, 2015
The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
Bruinier, Jan Hendrik +3 more
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The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
Bruinier, Jan Hendrik +3 more
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The Components of Modular Forms
Journal of the London Mathematical Society, 1995If \(f\) is a modular form on \(\text{SL}_2 (\mathbb{Z})\) of half-integral weight having \(q\) expansion \[ f(\tau):= q^\kappa \sum_{n\geq n_0} a_n q^n \] and \(m\) and \(k\) are integers with \(0\leq k< m\), we define the \((k,m)\)-th component of \(f\) to be the function \(f^{(k,m)}\) given by \[ f^{(k, m)} (\tau):= q^{(k+\kappa)/m} \sum_{nm+ k\geq ...
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Mathematische Nachrichten, 1997
AbstractWe study moduli spaces of principally polarized abelian varieties with an automorphism of finite order. After some examples (e. g. hermitian modular forms) we compute the ring of Picard modular forms in the case considered by Picard.
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AbstractWe study moduli spaces of principally polarized abelian varieties with an automorphism of finite order. After some examples (e. g. hermitian modular forms) we compute the ring of Picard modular forms in the case considered by Picard.
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Thetanullwerte and Stable Modular Forms
American Journal of Mathematics, 1989For g and k natural numbers, let \([\Gamma_ g,k]\) be the (complex) vector space of modular forms of degree g and weight k relative to the symplectic group \(\Gamma_ g:=Sp(g,{\mathbb{Z}})\). By \([\Gamma_ g,\vartheta,k]\) one defines the subspace of [\(\Gamma\),k] spanned over \({\mathbb{C}}\) by homogeneous polynomials of degree 2k in the ...
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Modular Groups and Modular Forms
1989In this chapter, we explain the general theory of modular forms. In §4.1, we discuss the full modular group SL 2(ℤ) and modular forms with respect to SL 2(ℤ), as an introduction to the succeeding sections. We define and study congruence modular groups in §4.2. In §4.3, we explain the relation between modular forms and Dirichlet series obtained by Hecke
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2014
The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
openaire +1 more source
The theory of Modular Forms has been central in mathematics with a rich history and connections to many other areas of mathematics. The workshop explored recent developments and future directions with a particular focus on connections to the theory of periods.
openaire +1 more source