Information retrieval (IR) in peer-to-peer (P2P) networks, where the corpus is spread across many loosely coupled peers, has recently gained importance. In contrast to IR systems on a centralized server or server farm, P2P IR faces the additional challenge of either being oblivious to global corpus statistics or having to compute the global measures from local statistics at the individual peers in an efficient, distributed manner. One specific measure of interest is the global document frequency for different terms, which would be very beneficial as term-specific weights in the scoring and ranking of merged search results that have been obtained from different peers. This paper presents an efficient solution for the problem of estimating global document frequencies in a large-scale P2P network with very high dynamics where peers can join and leave the network on short notice. In particular, the developed method takes into account the fact that the lo- cal document collections of autonomous peers may arbitrar- ily overlap, so that global counting needs to be duplicate- insensitive. The method is based on hash sketches as a technique for compact data synopses. Experimental stud- ies demonstrate the estimator?s accuracy, scalability, and ability to cope with high dynamics. Moreover, the benefit for ranking P2P search results is shown by experiments with real-world Web data and queries.