Modular forms for the A₁-tower

2017/06/19 by Woitalla, Martin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.05936

Abstract

In the 1960's Igusa determined the graded ring of Siegel modular forms of genus two. He used theta series to construct χ₅, the cusp form of lowest weight for the group Sp(2;Z). In 2010 Gritsenko found three towers of orthogonal type modular forms which are connected with certain series of root lattices. In this setting Siegel modular forms can be identifed with the orthogonal group of signature (2,3) for the lattice A₁ and Igusa's form χ₅ appears as the roof of this tower. We use this interpretation to construct a framework for this tower which uses three different types of constructions for modular forms. It turns out that our method produces simple coordinates for the graded rings of modular forms.

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