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Results tagged with analytic-number-theory
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user 172051
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.
10
votes
1
answer
472
views
A basic estimate of exponential sums
Demeter in his book "Fourier Restriction, Decoupling, and Applications" (P287) used the following estimate:
\begin{equation}
\sup_{0\leq n\leq q}\bigg|\sum_{m=0}^n e^{2\pi i\frac{a}{q}m^2}\bigg|\leq C …
- 351
8
votes
2
answers
809
views
Estimates about prime numbers: a lemma in Bourgain's article
For $n\in \mathbb{N}$ with prime decomposition $n=p_1^{r_1}\cdots p_k^{r_k},p_i\neq p_j$, let $A=\{p_1,\cdots,p_k\}$; then the following holds:
\begin{equation}
|\{q\in \mathbb{N},q<Q: \text{all prime …
- 351