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Results tagged with analytic-number-theory
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user 476460
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.
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Cardinality of a subset of smooth numbers
Recall: An $n$-smooth number is an integer whose prime factors are all less than or equal to $n$.
Let $k$ and $N$ two integers with $0\leq k\leq N$. Let's put $H= \{n\in[0,N]\ s.t.\ n\ is\ k-smooth\} …
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An estimate of a sum
I'm looking for an estimate of this sum $\sum_{n\leq x} \frac{\mu^2(n)}{\varphi(n)}$ where $\mu$ is the Möbius function and $\varphi$ the Euler's totient function.
Thanks a lot.
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Rough numbers in short interval
A positive integer $n$ is called $k$-rough if all of the prime factors of $n$ strictly exceed $k$.
For $k$ fixed and $n$ large, what's the shortest interval $[n,n+t]$ that contains a $k$-rough number …
- 43