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L. Ghezzi, , S. Goto, J. Hong, K. Ozeki, T.T. Phuong, and W. V. Vasconcelos (2010). Cohen–Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals. Journal of the London Mathematical Society, Volume 81 Issue 3 June 2010J. London Math. Soc. (2010) 81 (3): 679-695.
Abstract. The conjecture of Wolmer Vasconcelos on the vanishing of the first Hilbert coefficient e1(Q) is solved affirmatively, where Q is a parameter ideal in a Noetherian local ring. Basic properties of the rings for which e1(Q) vanishes are derived. The invariance of e1(Q) for parameter ideals Q and its relationship to Buchsbaum rings are studied.