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Differential modular forms [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2000 Summary: Algebraic geometry can be enlarged by adjoining a new operation, the Fermat quotient operation [cf. \textit{A. Buium}, Invent. Math. 122, 309--340 (1995; Zbl 0841.14037)]. This new geometry is an arithmetic analogue of the Ritt-Kolchin ``differential algebraic geometry''.
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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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Modular Forms on Schiermonnikoog
2008Modular forms are functions with an enormous amount of symmetry that play a central role in number theory, connecting it with analysis and geometry. They have played a prominent role in mathematics since the 19th century and their study continues to flourish today.
Edixhoven, B. +2 more
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Israel Journal of Mathematics, 1999
The author develops an algebraic theory of modular forms for connected reductive groups \(G\) over \(\mathbb Q\) with the property that every arithmetic subgroup \(\Gamma\) of \(G({\mathbb Q})\) is finite. This algebraic theory enables the author to define ``modular forms mod \(p\)'' for such groups.
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The author develops an algebraic theory of modular forms for connected reductive groups \(G\) over \(\mathbb Q\) with the property that every arithmetic subgroup \(\Gamma\) of \(G({\mathbb Q})\) is finite. This algebraic theory enables the author to define ``modular forms mod \(p\)'' for such groups.
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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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The Values of Modular Functions and Modular Forms
Canadian Mathematical Bulletin, 2006AbstractLet Γ0be a Fuchsian group of the first kind of genus zero and Γ be a subgroup of Γ0of finite index of genus zero. We find universal recursive relations giving theqr-series coefficients ofj0by using those of theqhs-series ofj, wherejis the canonical Hauptmodul for Γ andj0is a Hauptmodul for Γ0without zeros on the complex upper half plane(hereqℓ:=
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Onconephrology: The intersections between the kidney and cancer
Ca-A Cancer Journal for Clinicians, 2021Kenar D Jhaveri, Mark A Perazella
exaly
Mock modular forms and quantum modular forms
Proceedings of the American Mathematical Society, 2015Subong Lim +2 more
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