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Results tagged with analytic-number-theory
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user 60519
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.
9
votes
0
answers
513
views
Prime character sums
Let $p$ be a (large) prime number, and let $\chi : (\mathbf{Z}/p\mathbf{Z})^{\times} \rightarrow \mathbf{C}^{\times}$ be a Dirichlet character of conductor $p$. We have good estimates on the character …
- 1,109
19
votes
Elementary congruences and L-functions
I answer only for the $3$-part of your question (I have to think more for the $2$-part).
Let $N$ be a prime $\equiv 1 \text{ (mod } 3\text{)}$. Let $\text{log} : (\mathbf{Z}/N\mathbf{Z})^{\times} \ …
- 1,109
7
votes
1
answer
499
views
Smallest Mazur's good prime
Let $p$ and $\ell$ be primes $\geq 5$ such that $\ell$ divides $p-1$. Following Mazur, we say that a prime $q$ is a $\textit{good prime}$ if $\ell$ does not divide $q-1$ and $q$ is not a $\ell$th powe …
- 1,109