Spin 𝐿-functions on 𝐺𝑆𝑝₈ and 𝐺𝑠𝑝₁₀

Abstract

The “spin” L-function of an automorphic representation of G S p 2 n GSp_{2n} is an Euler product of degree 2 n 2^{n} associated with the spin representation of the L-group G S p i n ( 2 n + 1 ) \mathrm {GSpin}(2n+1) . If n = 4 n=4 or 5 5 , and the automorphic representation is generic in the sense of having a Whittaker model, the analytic properties of these L-functions are studied by the Rankin-Selberg method.