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Results tagged with analytic-number-theory
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user 113489
On the blending of real/complex analysis with number theory. The study involves distribution of prime numbers and other problems and helps giving asymptotic estimates to these.
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An exponential sum estimate on small intervals
Let $1<r<2$ be a real number. Let $4<p\le 6$. Consider the exponential sum estimate
$$\int_0^{2\pi}\int_0^{N^{r-2}} \left|\sum_{n=1}^N e^{inx+in^2 y}\right|^p \, dy \, dx$$
Notice that the $y$ variabl …
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