Differential Geometry (01) by Helgason, Sigurdur [Hardcover

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Indeed, already c. 1947, Maass showed that real quadratic fields' grossencharacter L-functions arose as Mellin transforms of "waveforms", Laplace-Beltrami eigenfunctions on $\Gamma\backslash H$, a complementary result to his advisor Hecke's result that $L$-functions for complex quadratic extensions of $\mathbb Q$ arose from holomorphic modular forms. As classical as the subject is, it is currently undergoing a very vigorous development, interacting strongly with theoretical physics, mechanics, topology, algebraic geometry, symplectic topology, partial differential equations, the calculus of variations, integrable systems, and many other subjects.

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Publisher: American Mathematical Society, Hardcover(2001) (2001)


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