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Mock theta functions and indefinite modular forms (2206.02293v6)
Published 6 Jun 2022 in math.NT and math.RT
Abstract: In the explicit formula for the signed mock theta functions $\Phi{(-)[m,s]}$ obtained from the coroot lattice of $D(2,1;a)$, functions with indefinite quadratic forms naturally take place. We compute their modular transformation properties by applying the Zwegers' modification theory of mock theta functions and show that the $\mathbf{C}$-linear span of these functions is $SL_2(\mathbf{Z})$-invariant.