A Bibliometric and Topic Modeling Analysis of the p-Adic Theory Literature Using Latent Dirichlet Allocation

P-adic analysis, introduced by Kurt Hensel in the early 20th century, has developed into a fundamental area of mathematical research with broad applications in number theory, algebraic geometry, and mathematical physics. This study aims to examine the thematic evolution and scholarly impact of p-adic research through a comprehensive topic modeling and bibliometric analysis. Using classical bibliometric techniques (e.g., performance analysis, co-authorship, and co-citation networks) combined with Latent Dirichlet Allocation (LDA), we analyzed 7388 peer-reviewed documents published between 1965 and 2024. The computational workflow was conducted using R (version 4.4.1) and VOSviewer (version 1.6.20), which enabled the identification of 20 distinct research topics. These topics reveal both well-established and emerging areas, such as p-adic differential equations, harmonic analysis, and their connections to theoretical physics and cryptography. This study highlights key contributors, including Robert Coleman, Alain M. Robert, and Jean-Pierre Serre, whose work has shaped the development of the field. Temporal patterns observed in the topic distribution indicate dynamic shifts in research focus, while the interdisciplinary nature of recent contributions highlights the growing relevance of p-adic theory beyond pure mathematics. This analysis provides a data-driven overview of the intellectual structure of p-adic research, identifies underexplored areas, and suggests future directions for inquiry. The findings aim to support researchers in understanding historical trends, recognizing influential work, and identifying opportunities for further advancement and collaboration in the field.