A collection of manuscripts written in honour of John H. Coates on the occasion of his sixtieth birthday

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This volume is dedicated to Professor John H. Coates, a significant figure in number theory, recognized for his pioneering contributions and the mathematical school he established. It features 24 articles by 38 authors, covering a wide array of contemporary research topics in number theory, algebraic geometry, and analysis, including zeta functions, L-functions, automorphic forms, Galois representations, and the arithmetic of elliptic curves. Among the contributions are: - K. Ardakov and K. A. Brown's survey on ring-theoretic properties of Iwasawa algebras. - G. Banaszak and colleagues' exploration of l-adic Galois representations for abelian varieties. - S. Böcherer and A. A. Panchishkin's work on p-adic measures related to elliptic cusp forms. - David Burns and Matthias Flach's examination of the equivariant Tamagawa number conjecture. - Kevin Buzzard and Frank Calegari's insights into the 2-adic eigencurve. Additional topics include Galois cohomology, p-adic L-functions, and modular representations. This volume will appeal to researchers and students in these fields and related areas, providing a comprehensive overview of current advancements and methodologies in number theory and its applications.