ArchimedeanL-factors onGL(n) ×GL(n) and generalized Barnes integrals

By E. Stade. 2002

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Mellin transforms of GL(n, R) whittaker functions (2001, unknown): “(See, for example, [2], [10], [11], [13], [17], [20], [21].”
On the Exceptional Zeros of Rankin–Selberg L-Functions (2001, methodology): “als. Thus I is in fact the same as the quotient of the complete L-series for Π×Π by L(1,Π∞ × Π∞). Note that the Whitaker function at inﬁnity we take here diﬀers from the standard one used by Stade in [St2001] by the factor C(Π)−1/2. Now take the residue at s = 1 on both sides, and note that Ress=1E∗”
Directed polymers and the quantum Toda lattice (2009, background): “This is closely related to a Whittaker integral identity which was conjectured by Bump [9] and later proved by Stade [56], Theorem 1.”
Tropical Combinatorics and Whittaker functions (2011, background): “We remark that, while this gives a new interpretation of the Bump-Stade Whittaker integral identity, we do not give a new proof of this identity in the present paper; in fact, we use it to obtain the simplification (1.3).”
Correlation functions in conformal Toda field theory I (2007, background): “The problem of finding the Fourier transform of the product of two Whittaker functions was considered in [43].”