An example of Whimsical identity is the global Langlands correspondence: elliptic curves should not be the only objects from arithmetic geometry with L-functions related to harmonic analysis on algebraic groups. In fact many conjectures in arithmetic geometry are of this kind: Deligne-Beilinson conjectures on special values of L-functions, description of the image of Galois on etale cohomology groups in terms of the Mumford-Tate group, etc.
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