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Results tagged with analytic-number-theory
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user 2481
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.
12
votes
1
answer
528
views
Roots of unity near 1 in Z / p Z
Let $r \ge 3$ be a fixed integer. I'm interested in primes p such that no integer in the interval $(-\sqrt{p}, \sqrt{p})$, except $1$ (and $-1$ if $r$ is even), is an r-th root of unity modulo p.
The …
- 37k
5
votes
2
answers
126
views
Residue of Dirichlet series at $s = 1$
Let $(a_n)_{n \ge 1}$ be a sequence of complex numbers, and suppose that the sequence has a well-defined "average", in the sense that
$$ \lim_{N \to \infty} \frac{1}{N}\sum_{i = 1}^N a_i = R$$
for som …
- 37k