Question

Prove $\sum_{n=1}^{\infty}\frac{\nu(n)}{n^s}=\zeta(s)\sum_p\frac{1}{p^s}$.

score 90 · Answer 1 · 2026-04-15 13:43:23

90

Views

Prove $\sum_{n=1}^{\infty}\frac{\nu(n)}{n^s}=\zeta(s)\sum_p\frac{1}{p^s}$.

Published on 15 Apr 2026 - 13:43

score 65 · Answer 2 · 2026-04-14 11:24:34

65

Views

Solutions to an elliptic curve equation involving a prime

Published on 14 Apr 2026 - 11:24

score 109 · Answer 3 · 2026-04-09 18:29:34

109

Views

Sum of Dirichlet characters

Published on 09 Apr 2026 - 18:29

score 121 · Answer 4 · 2026-04-14 16:30:05

121

Views

Length of this representation increases really slowly?

Published on 14 Apr 2026 - 16:30

score 47 · Answer 5 · 2026-04-10 05:02:58

47

Views

Boundedness of Liouville function sum

Published on 10 Apr 2026 - 5:02

score 111 · Answer 6 · 2026-04-17 11:20:39

111

Views

$\varphi(x)\sim x$ then $\psi_1(x)\sim x^2/2$

Published on 17 Apr 2026 - 11:20

score 82 · Answer 7 · 2026-04-15 14:13:53

82

Views

Prove that the analytic mean value of an arithmetic function equals the logarithmic mean value

Published on 15 Apr 2026 - 14:13

score 65 · Answer 8 · 2026-04-16 04:45:57

65

Views

Use Taylor's theorem to derive an expression for $\log\left(1-\frac{1}{(n+1)^\alpha}\right)-\log\left(1-\frac{1}{n^\alpha}\right)$

Published on 16 Apr 2026 - 4:45

score 70 · Answer 9 · 2026-04-14 16:18:57

70

Views

Prove that a set $\mathcal{H}$ is admissible if it's composed of $k_0$ distinct primes, each bigger than $k_0$

Published on 14 Apr 2026 - 16:18

score 35 · Answer 10 · 2026-04-12 00:45:22

35

Views

interesting relationship involving the growth of differences between log integral and prime counting function

Published on 12 Apr 2026 - 0:45

score 114 · Answer 11 · 2026-04-13 16:14:27

114

Views

Relating the two errors terms in the prime number theorem

Published on 13 Apr 2026 - 16:14

score 91 · Answer 12 · 2026-04-12 06:15:25

91

Views

Size of a Mellin integral

Published on 12 Apr 2026 - 6:15

score 63 · Answer 13 · 2026-04-13 20:52:53

63

Views

Estimates for the norm of the $p$-adic Iwasawa logarithm

Published on 13 Apr 2026 - 20:52

score 71 · Answer 14 · 2026-04-12 16:39:01

71

Views

Switching of summation indices in Analytic Number Theory

Published on 12 Apr 2026 - 16:39

score 67 · Answer 15 · 2026-04-17 11:25:52

67

Views

Why is $\sum_{m=1}^{n}\frac{(\nu(m)-\log\log n)^2}{n\log\log n}=\int_{-\infty}^{\infty}\omega^2\, \mathrm{d}\sigma_n(\omega)$?

Published on 17 Apr 2026 - 11:25

List Question

Prove $\sum_{n=1}^{\infty}\frac{\nu(n)}{n^s}=\zeta(s)\sum_p\frac{1}{p^s}$.

Solutions to an elliptic curve equation involving a prime

Sum of Dirichlet characters

Length of this representation increases really slowly?

Boundedness of Liouville function sum

$\varphi(x)\sim x$ then $\psi_1(x)\sim x^2/2$

Prove that the analytic mean value of an arithmetic function equals the logarithmic mean value

Use Taylor's theorem to derive an expression for $\log\left(1-\frac{1}{(n+1)^\alpha}\right)-\log\left(1-\frac{1}{n^\alpha}\right)$

Prove that a set $\mathcal{H}$ is admissible if it's composed of $k_0$ distinct primes, each bigger than $k_0$

interesting relationship involving the growth of differences between log integral and prime counting function

Relating the two errors terms in the prime number theorem

Size of a Mellin integral

Estimates for the norm of the $p$-adic Iwasawa logarithm

Switching of summation indices in Analytic Number Theory

Why is $\sum_{m=1}^{n}\frac{(\nu(m)-\log\log n)^2}{n\log\log n}=\int_{-\infty}^{\infty}\omega^2\, \mathrm{d}\sigma_n(\omega)$?

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