Logarithmic vector-valued modular forms

Marvin Knopp; Geoffrey Mason

Displaying similar documents to “Logarithmic vector-valued modular forms”

On values of a modular form on Γ₀(N)

D. Choi (2006)

Acta Arithmetica

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On the finiteness of $S h$ for motives associated to modular forms.

Besser, Amnon (1997)

Documenta Mathematica

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Vector-valued modular forms associated to linear ordinary differential equations

Min Ho Lee (2008)

Commentationes Mathematicae Universitatis Carolinae

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We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.

Generalized modular spaces

Hidegoro Nakano (1968)

Studia Mathematica

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Vector Valued Siegel's Modular Forms of Degree Two and the Associated Andrianov L-Functions.

Tsuneo Arakawa (1983)

Manuscripta mathematica

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Modular equations for some η-products

(2013)

Acta Arithmetica

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The classical modular equations involve bivariate polynomials that can be seen to be univariate in the modular invariant j with integer coefficients. Kiepert found modular equations relating some η-quotients and the Weber functions γ₂ and γ₃. In the present work, we extend this idea to double η-quotients and characterize all the parameters leading to this kind of equation. We give some properties of these equations, explain how to compute them and give numerical examples.