Modular forms of half-integral weight on exceptional groups

2022/05/30 by Leslie, Spencer, Pollack, Aaron · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.15391

Abstract

We define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by ± 1. We analyze the minimal modular form Θ_F4 on the double cover of F₄, following Loke--Savin and Ginzburg. Using Θ_F4, we define a modular form of weight (1)/(2) on (the double cover of) G₂. We prove that the Fourier coefficients of this modular form on G₂ see the 2-torsion in the narrow class groups of totally real cubic fields.

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• Generalized Whittaker models beyond \mathfraksl₂-triples

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• The Fourier expansion of modular forms on quaternionic exceptional groups
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