ATS Theorem - Remark


If the parameters and are integers, then it is possible to substitute the last relation by the following ones:

\sum_{a<k\le b} e^{2\pi i f(k)} = \int_a^be^{2\pi i f(x)}dx +
\frac12e^{2\pi i f(b)} - \frac12e^{2\pi i f(a)} +


On the applications of ATS to the problems of physics see,; see also,.

Read more about this topic:  ATS Theorem

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