@article{Connes2011TheHO,
author={Alain Connes and Caterina Consani},
journal={Journal of Number Theory},
year={2011},
volume={131},
pages={159-194}
}`
• Published 1 February 2011
• Mathematics
• Journal of Number Theory
88 Citations

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From monoids to hyperstructures: in search of an absolute arithmetic

• Mathematics
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We show that the trace formula interpretation of the explicit formulas expresses the counting functionN.q/ of the hypothetical curveC associated to the Riemann zeta function, as an intersection

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We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this idea to the notion

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