I can think of the following:
Friedman, J. (2001). Greedy boosting approximation: a gradient
boosting machine. Ann. Stat. 29, 1189–1232. doi:
10.1214/aos/1013203451 link
Friedman, J., Hastie, T., and Tibshirani, R. (2000). Additive logistic
regression: a statistical view of boosting. Ann. Stat. 28, 337–407.
doi: 10.1214/aos/1016218222 link
J. H. Friedman. Stochastic gradient boosting. Computational Statistics
and Data Analysis, 38(4):367–378, 2002. link
Friedman, Hastie, and Tibshirani (2000) paper discusses the first successful boosting algorithm, Adaboost from a statistical point of view. Friedman (2001) and the companion paper Friedman (2002) extended the work to generalize Adaboost to Gradient Boosting in order to handle a variety of loss functions.
There is a paper I came across but haven't had the chance to go in depth:
(May 4) David Mease and Abraham Wyner (2008). Evidence contrary to the
statistical view of boosting. Journal of Machine Learning Research,
vol 9, pp 131--156 link