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Results tagged with analytic-number-theory
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user 493567
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.
3
votes
0
answers
163
views
Green-Tao's "Polylogarithmic bound for $r_4(N)$"
On P.23 of https://arxiv.org/pdf/1705.01703.pdf, they seemed to suggest that by the non-negativity of $\psi\big(\frac{k}{N}\big)$ for all $k$,
$$
K_N(\xi_0 n)\left[1-\cos\bigg(\frac{2\pi\xi_0 n}{p}\bi …
- 53
2
votes
1
answer
177
views
Modified Gauss Sum when the characters have different period
Let $\chi$ be a Dirichlet character mod q, and
\begin{eqnarray}
t(\chi)=\sum_{n=1}^{q}\chi(n)e(\frac{n}{2q}).
\end{eqnarray}
Do we have a bound or formula for $t(\chi)$ similar to that of the usual Ga …
- 53