Abstract
The anomalous magnetic moment of the electron is one of the physical quantities measured with the highest precision. Such high precision demands a similar precision in the theoretical evaluations in order to obtain stringent tests of QED. In this talk I will summarize the situation of the theoretical calculations of the contributions to the electron g-2; then, I will describe in detail the results of the twenty-year long project of the evaluation of all the 891 mass-independent four-loop QED Feynman diagrams contributing to the electron g-2 [11], with the 1100-digits result and high-precision analytical fits. The consequences of this result on the QED tests and the determination of the fine structure constant will be also discussed.
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