Abstract: In 2014, Gelbart, Miller, Panchishkin, and Shahidi introduced a p-adic analog to part of the Langlands-Shahidi method by studying the reciprocal of the p-adic L-function through the Fourier series expansion of Eisenstein series on SL_2(Z). In this talk, I discuss an analogous result in the case where K is a totally real number field. More precisely, I will construct a certain p-adic measure whose Mellin transform is the reciprocal of the Deligne-Ribet p-adic L-function. This construction arises from the analysis of the non-constant Fourier coefficients of the Eisenstein series on the Hilbert modular group SL_2(O_K).