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The method of exponential sums is one of a few general methods enabling us to solve a wide range of miscellaneous problems from the theory of numbers and its applications. The strongest results have been obtained with the aid of this method. Therefore knowledge of the fundamentals of theory of exponential sums is necessary for studying modern number theory.

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Product of three or more independent sub-Gaussian varibles

As indicated in the comment, the boundedness can be used to prove that the product is sub-Gaussian. Suppose $X_{1}, \ldots, X_{n}$ are bounded such that for $i \in [n]$ there exists a constant such th …
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