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Results tagged with analytic-number-theory
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user 23827
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.
6
votes
2
answers
629
views
Rate of convergence of the prime zeta function P(2)
For an application in statistical group theory, we need explicit upper and lower bounds that an expert in number theory (I am not one) may know how to prove.
Question 1: What are "good" bounds $f_1(x …
- 105
4
votes
Rate of convergence of the prime zeta function P(2)
An answer to Question 2 follows from the lemma below by letting $y\to\infty$.
Lemma. Suppose $x,y$ are real numbers with $12\leqslant x\leqslant y$ and $p$ denotes a prime. Then
$$\sum_{x<p\leqslant y …
- 105