Harish-Chandra's Ξ function

Harish-Chandra's Ξ function, often denoted as \( \Xi(s) \), is a special function in the field of representation theory and number theory, related to automorphic forms and the theory of L-functions. It is particularly significant in the study of the spectral decomposition of automorphic forms and the Langlands program. Specifically, the Ξ function emerged in the context of automorphic representations of reductive groups over global fields.