Fourier Analysis on Number Fields

The book "Fourier Analysis on Number Fields" offers a comprehensive and modern approach to number theory, developed from the author's lecture notes over several years at renowned universities. It combines algebraic and analytical perspectives, placing a particular emphasis on harmonic analysis on topological groups. A central aim 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 adopts a thorough and accessible approach. It is aimed at students who have already completed a year of graduate courses in algebra, analysis, and topology, and is significant for both aspiring number theorists and students of harmonic analysis and representation theory of Lie groups.