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A standard measure of the influence of a research paper is the number of times it is cited. However, papers may be cited for many reasons, and citation count offers limited information about the extent to which a paper affected the content of subsequent publications. We therefore propose a novel method to quantify linguistic influence in timestamped document collections. There are two main steps: first, identify lexical and semantic changes using contextual embeddings and word frequencies; second, aggregate information about these changes into per-document influence scores by estimating a high-dimensional Hawkes process with a low-rank parameter matrix. We show that this measure of linguistic influence is predictive of future citations: the estimate of linguistic influence from the two years after a paper’s publication is correlated with and predictive of its citation count in the following three years. This is demonstrated using an online evaluation with incremental temporal training/test splits, in comparison with a strong baseline that includes predictors for initial citation counts, topics, and lexical features.