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We refine and extend previous constructions of $p$-adic $L$-functions forRankin-Selberg convolutions on $\GL(n)\times\GL(n-1)$ for regular algebraicrepresentations over totally real fields. We also prove an intrinsic functionalequation for this $p$-adic $L$-function, which will be of interest in furtherstudy of its arithmetic properties.

On p-adic L-functions for ${\rm GL}(n)\times{\rm GL}(n-1)$ over totally real fields