Shor's algorithm

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Shor's algorithm factorizes a large n digit integers in 0(n^3) elementary operations on an hypothetical quantum computer. The aim of the talk is to present the mathematical aspects of the algorithm (structure of the multiplicative group of units in cyclic groups, the Fourier transform on cyclic groups, tensor products of finite dimensional Hilbert spaces, continued fractions, estimates of the Euler function) and to explain how the algorithm works.