An Essay on the Riemann Hypothesis

2016/01/01 by Alain Connes · 16 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic geometry #Cohomology #Geometry and topology #Homotopy and Cohomology in Algebraic Topology #Mathematics #Noncommutative geometry #Pure mathematics #Riemann surface

paper · doi:10.1007/978-3-319-32162-2_5

published in Open Problems in Mathematics, 225-257 (Springer International Publishing)

crossref issued 2016/01/01 · crossref published 2016/01/01 · crossref published-print 2016/01/01 · openalex publication_date 2016/01/01 · crossref created 2016/07/05 · crossref published-online 2016/07/06 · crossref deposited 2023/08/19 · openalex created_date 2025/10/10 · crossref indexed 2026/04/21 · openalex updated_date 2026/08/04

Citations

• Sur une note de Mattuck-Tate.
• New Approach to Arakelov Geometry
• The Classical Theory of Zeta and L-Functions
• A geometric approach to the representations of the full linear group over a Galois field
• A Lefschetz Fixed Point Formula for Elliptic Complexes: I
• The Selberg trace formula and the Riemann zeta function
• The Positivity of a Sequence of Numbers and the Riemann Hypothesis
• Sur la Théorie du Corps de Classes
• An Introduction to the Theory of the Riemann Zeta-Function
• Chip-firing Games on Graphs
• La conjecture de Weil : I
• Trace formula in noncommutative geometry and the zeros of the Riemann zeta function
• On a representation of the idele class group related to primes and zeros of L-functions
• On the p-typical curves in Quillen's K-theory
• The Radical and Semi-Simplicity for Arbitrary Rings
• Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory

Cited by

• Riemann hypothesis [wikipedia]