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Motivic Rhythms
Alain Connes
In this article on mathematics and music, we explain how one can "listen to motives" as rhythmic interpreters. In the simplest instance which is the one we shall consider, the moti…
The Carlitz group of the rationals
Alain Connes
This paper contains two parts. The first is the solution of a challenge question, proposed by Etienne Ghys, on the determination of all maps from rational numbers to themselves suc…
Around Wilson's theorem
Alain Connes
We study the series s(n,x) which is the sum for k from 1 to n of the square of the sine of the product x Gamma(k)/k, where x is a variable. By Wilson's theorem we show that the int…
The Riemann-Roch strategy, Complex lift of the Scaling Site
Alain Connes, Caterina Consani
We describe the Riemann-Roch strategy which consists of adapting in characteristic zero Weil's proof, of RH in positive characteristic, following the ideas of Mattuck, Tate and Gro…