1.4k citations · 8.5k across the 104 of their papers we have counts for
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math.AG2009★ 36 cited
Characteristic one, entropy and the absolute point
Alain Connes, Caterina Consani
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…
math.QA2009★ 68 cited
The Gauss-Bonnet Theorem for the noncommutative two torus
Alain Connes, Paula Tretkoff
In this paper we show that the value at zero of the zeta function of the Laplacian on the non-commutative two torus, endowed with its canonical conformal structure, is independent…
math.AG2009★ 79 cited
Schemes over $\F_1$ and zeta functions
Alain Connes, Caterina Consani
We determine the {\em real} counting function () for the hypothetical "curve" $C=\overline {\Sp \Z}$ over $\F_1$, whose corresponding zeta function is the c…