An essay on the Riemann Hypothesis

  title={An essay on the Riemann Hypothesis},
  author={Connes Alain},
  journal={arXiv: Number Theory},
  • Connes Alain
  • Published 18 September 2015
  • Mathematics
  • arXiv: Number Theory
The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to uncover and explore new parts of the mathematical world. After reviewing its impact on the development of algebraic geometry we discuss three strategies, working concretely at the level of the explicit formulas. The first strategy is "analytic" and is based on Riemannian spaces and Selberg's work on the trace formula and its comparison with the explicit formulas. The second is based on algebraic geometry… 
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