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Abstract The zeta function of an arbitrary field in (d + 1)-dimensional anti-de Sitter (AdS) spacetime is expressed as an integral transform of the corresponding so(2, d) representation character, thereby extending the results of [ arXiv:1603.05387 ] for AdS4 and AdS5 to arbitrary dimensions. The integration in the variables associated with the so(d) part of the character can be recast into a more explicit form using derivatives. The explicit derivative expressions are presented for AdS d+1 with d = 2, 3, 4, 5, 6.