1997/10/01 by D. Zagier, Don Zagier · 1 citation
Mathematics · #Algebra over a field #Analytic number theory #Analytic proof #Calculus (dental) #Combinatorics #Compactness theorem #Discrete mathematics #Elementary proof #Fixed-point theorem #Fundamental theorem #History and Theory of Mathematics #Mathematical proof #Mathematics #Multiplicative number theory #Number theory #Prime (order theory) #Prime factor #Prime number #Prime number theorem #Proofs of Fermat's little theorem #Pure mathematics #Riemann hypothesis #Simple (philosophy)
paper · doi:10.1080/00029890.1997.11990704
crossref issued 1997/10/01 · crossref published 1997/10/01 · crossref published-print 1997/10/01 · openalex publication_date 1997/10/01 · crossref published-online 2018/04/10 · crossref created 2018/04/10 · openalex created_date 2025/10/10 · crossref deposited 2026/01/29 · crossref indexed 2026/06/20 · openalex updated_date 2026/08/03
This three-page article contains a complete proof of the prime number theorem, starting with the zeta series, and ending with it D. J. Newman's Tauberian theorem [Am. Math. Mon. 87, 693-696 (1980; Zbl 0444.10033)]. A shorter approach can hardly be imagined.