Fourier Analysis on Number Fields

The book "Fourier Analysis on Number Fields" offers a comprehensive and modern approach to number theory, characterized by the combination of algebraic and analytical perspectives. It is based on notes from several courses that the author taught over a period of nine years at prestigious universities. The main goal of the book is to provide a detailed treatment of John Tate's visionary dissertation and to convey the necessary analytical and topological foundations that are often unfamiliar to algebraically oriented number theorists. Unlike other treatments of Tate's dissertation, which are often brief or cryptic, this work takes a thorough and accessible approach. It is aimed at students who have already completed a year of graduate courses in algebra, analysis, and topology, making it of interest to both aspiring number theorists and students of harmonic analysis or representation theory of Lie groups.