Introduction to zeta integrals and L-functions for GLn
نویسنده
چکیده
All known ways to analytically continue automorphic L-functions involve integral representations using the corresponding automorphic forms. The simplest cases, extending Hecke’s treatment of GL2, need no further analytic devices and very little manipulation beyond Fourier-Whittaker expansions. [1] Poisson summation is a sufficient device for several accessible classes of examples, as in Riemann, [Hecke 1918,20], [Tate 1950], [Iwasawa 1952], and [Godement-Jacquet 1972], and including treatment of the degenerate Eisenstein series needed for the GLn ×GLn Rankin-Selberg convolutions. [2] For f a cuspform on GLn the most natural L-function obtained by an integral representation is the Hecke-type integral representation, also involving a cuspform F on GLn−1,
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