List questions from mobius-inversion

Published on 12 Apr 2026 - 5:28

510

Views

On Mertens function as $2 \sum_{k=1}^{N} \sum_{n=1}^{\infty}\frac{\mu(n)}{n} \sum_{m=1}^{\infty}\frac{(\mu(k))^{nm}}{m2^{nm}} $

Published on 14 Apr 2026 - 20:57

225

Views

Mobius inversion formula

Published on 10 Apr 2026 - 10:38

185

Views

Bernoulli numbers, primes, integers and the Möbius function

Published on 10 Apr 2026 - 12:57

266

Views

Evaluate $\int_0^1 \frac{\log(1-z)\log(1-z^3)}{z^2}dz$

Published on 16 Apr 2026 - 16:15

240

Views

Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

Published on 16 Apr 2026 - 19:59

860

Views

Number of relatively prime pairs in a range

Published on 16 Apr 2026 - 9:41

271

Views

Proving Mobius formula for cyclotomic polynomials without using $x^{n} - 1 = \prod_{d \mid n} \Phi_d(x)$

Published on 17 Apr 2026 - 13:48

87

Views

Prove by strong induction that if $\sum_{d\mid n} f(d) =F(n)$, and $F(n)$ is multiplative, then so is $f(n)$

Published on 14 Apr 2026 - 22:45

112

Views

Möbius Inversion with Additional Term

Published on 11 Apr 2026 - 13:46

1k

Views

show that $ \sum_{p \leq x} \log p \big( \log x - \log p\big) = O(x) $

Published on 17 Apr 2026 - 8:16

70

Views

Proving non-negativity of möbius inversion of set function

Published on 13 Apr 2026 - 13:26

127

Views

On the behaviour of $\sum_{\substack{n\leq x\\(n,k)=1}}\frac{1}{\sqrt[\alpha]{n}}$

Published on 16 Apr 2026 - 2:20

809

Views

Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

Published on 10 May 2026 - 14:29

200

Views

If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

Published on 25 Mar 2026 - 13:05

List Question

What's about $\sum_{n=1}^\infty\frac{\mu(n)}{n}r^n,$ when $0<r<1$?

On Mertens function as $2 \sum_{k=1}^{N} \sum_{n=1}^{\infty}\frac{\mu(n)}{n} \sum_{m=1}^{\infty}\frac{(\mu(k))^{nm}}{m2^{nm}} $

Mobius inversion formula

Bernoulli numbers, primes, integers and the Möbius function

Evaluate $\int_0^1 \frac{\log(1-z)\log(1-z^3)}{z^2}dz$

Evaluate $\int_0^\infty\left\{ \frac{1}{t} \right\}^{kn}t^{s-1}dt$ for positive integers $n,k$ and $0<\Re s<1$

Number of relatively prime pairs in a range

Proving Mobius formula for cyclotomic polynomials without using $x^{n} - 1 = \prod_{d \mid n} \Phi_d(x)$

Prove by strong induction that if $\sum_{d\mid n} f(d) =F(n)$, and $F(n)$ is multiplative, then so is $f(n)$

Möbius Inversion with Additional Term

show that $ \sum_{p \leq x} \log p \big( \log x - \log p\big) = O(x) $

Proving non-negativity of möbius inversion of set function

On the behaviour of $\sum_{\substack{n\leq x\\(n,k)=1}}\frac{1}{\sqrt[\alpha]{n}}$

Invert: $\sum\limits_{d|n} \mu(d) \lambda(d)=2^{\omega(n)}$

If $a$ is the arithmetic function with $\sum_{d\mid n}a(d)=2^n$, then $n\mid a(n)$

Trending Questions

Popular # Hahtags

Popular Questions