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We describe a new perspective on the intersection theory of the moduli spaceof curves involving both Virasoro constraints and Gorenstein conditions. Themain result of the paper is the computation of a basic 1-point Hodge integralseries occurring in the tautological ring of the moduli space of nonsingularcurves.  In the appendix by D. Zagier, "Polynomials arising from the tautologicalring", a detailed study is made of certain polynomials whose coefficients areintersection numbers on moduli space. The paper and the appendix togetherprovide proofs of all previously conjectured formulas for 1-point integrals inthe tautological ring, and of natural extensions of these formulas as well.

Logarithmic series and Hodge integrals in the tautological ring. With an appendix by Don Zagier.