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2017•Mathematische AnnalenOpen access

Covariants of binary sextics and vector-valued Siegel modular forms of genus two

Fabien Cléry, Carel Faber, Gerard van der Geer

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Abstract

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2.

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What this paper is about

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2.

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Available abstract

We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2.

Key concepts: Siegel modular form, Mathematics, Degree (music), Pure mathematics, Modular design, Binary number, Genus, Modular form

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