Classical pluriharmonic theta functions give one a way to explicitly write down cuspidal holomorphic (Siegel) modular forms, together with their exact Fourier expansion. These classical theta functions are associated to algebraic modular forms on definite orthogonal groups. I will describe an "exceptional" analogue of these classical theta functions, which are associated to algebraic modular forms on definite forms of the exceptional groups G_2 and F_4. I will also describe some applications.

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