Question

How to get the Euler product for $\sum_{n = 1}^{\infty} \mu(n)/\phi(n^k)$.

score 71 · Answer 1 · 2026-03-25 22:03:26

71

Views

How to get the Euler product for $\sum_{n = 1}^{\infty} \mu(n)/\phi(n^k)$.

Published on 25 Mar 2026 - 22:03

score 51 · Answer 2 · 2023-05-23 08:49:16

51

Views

Proving Gauss' Triangular Number Theorem from Apostol

Published on 23 May 2023 - 8:49

score 65 · Answer 3 · 2026-03-26 18:40:55

65

Views

Question of the order of growth

Published on 26 Mar 2026 - 18:40

score 83 · Answer 4 · 2026-02-23 07:45:12

83

Views

Any $n$ distinct positive integers always have three of them with large least common multiple

Published on 23 Feb 2026 - 7:45

score 62 · Answer 5 · 2023-06-04 18:10:38

62

Views

Unable to Understand Notations in Davenport's MNT

Published on 04 Jun 2023 - 18:10

score 39 · Answer 6 · 2026-03-30 03:56:22

39

Views

Number of Classes in a Genus of a Quadratic Form?

Published on 30 Mar 2026 - 3:56

score 31 · Answer 7 · 2023-06-06 12:37:21

31

Views

Meromorphic continuation of an integral similar to Tate integral

Published on 06 Jun 2023 - 12:37

score 114 · Answer 8 · 2023-06-07 20:01:11

114

Views

How can we prove that $\lim_{x\to\infty}\left(\frac{\pi (x)}{x}-\frac{1}{\log x}\right)=0$?

Published on 07 Jun 2023 - 20:01

score 96 · Answer 9 · 2026-03-28 20:14:32

96

Views

Bizarre function that generalizes the inclusion-exclusion formula for $\pi(t) - \pi(\sqrt{t + 1})$. For all reals $t\geq 5$, the function is non-zero

Published on 28 Mar 2026 - 20:14

score 71 · Answer 10 · 2023-06-09 20:40:35

71

Views

abscissa of convergence of $\sum_{n = 1}^\infty \frac{\mu(n)}{n^s}$

Published on 09 Jun 2023 - 20:40

score 94 · Answer 11 · 2023-06-10 05:04:05

94

Views

Is the integer with the largest number of divisors uniformly distributed in a prime gap?

Published on 10 Jun 2023 - 5:04

score 56 · Answer 12 · 2023-06-12 02:15:57

56

Views

Query on Apostol's definition of the derivative of Arithmetical functions

Published on 12 Jun 2023 - 2:15

score 277 · Answer 13 · 2026-03-25 16:20:37

277

Views

Is the function for the Weak Goldbach Conjecture an increasing function?

Published on 25 Mar 2026 - 16:20

score 84 · Answer 14 · 2026-04-01 22:19:04

84

Views

What is the closed form of the infinite series $g(x) = \sum_{r=1}^{\infty} x^{3^{r}}$ for $|x|<1$?

Published on 01 Apr 2026 - 22:19

score 52 · Answer 15 · 2026-03-28 08:47:49

52

Views

Integral identity satisfied by complex function

Published on 28 Mar 2026 - 8:47

List Question

How to get the Euler product for $\sum_{n = 1}^{\infty} \mu(n)/\phi(n^k)$.

Proving Gauss' Triangular Number Theorem from Apostol

Question of the order of growth

Any $n$ distinct positive integers always have three of them with large least common multiple

Unable to Understand Notations in Davenport's MNT

Number of Classes in a Genus of a Quadratic Form?

Meromorphic continuation of an integral similar to Tate integral

How can we prove that $\lim_{x\to\infty}\left(\frac{\pi (x)}{x}-\frac{1}{\log x}\right)=0$?

Bizarre function that generalizes the inclusion-exclusion formula for $\pi(t) - \pi(\sqrt{t + 1})$. For all reals $t\geq 5$, the function is non-zero

abscissa of convergence of $\sum_{n = 1}^\infty \frac{\mu(n)}{n^s}$

Is the integer with the largest number of divisors uniformly distributed in a prime gap?

Query on Apostol's definition of the derivative of Arithmetical functions

Is the function for the Weak Goldbach Conjecture an increasing function?

What is the closed form of the infinite series $g(x) = \sum_{r=1}^{\infty} x^{3^{r}}$ for $|x|<1$?

Integral identity satisfied by complex function

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