Modular forms of half-integral weight on exceptional groups
Spencer Leslie,
Aaron Pollack
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
${\pm }1$
. We analyze the minimal modular form
$\Theta _{F_4}$
on the double cover of
$F_4$
, following Loke–Savin and Ginzburg. Using
$\Theta _{F_4}$
, we define a modular for… Show more
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