Question

Find the integral values for which $\left(\pi(x+y)\right)^2=4\pi(x)\pi(y)$

score 135 · Answer 1 · 2015-01-08 15:15:08

135

Views

Find the integral values for which $\left(\pi(x+y)\right)^2=4\pi(x)\pi(y)$

Published on 08 Jan 2015 - 15:15

score 101 · Answer 2 · 2015-01-08 19:07:51

101

Views

Number of the positive integers up to $\sqrt x $ generated by the prime factors of $x$.

Published on 08 Jan 2015 - 19:07

score 64 · Answer 3 · 2015-01-13 13:10:52

64

Views

Is the integral $\int_1^{\infty} {A(t)}{t^{-s-1}}dt$ a holomorphic function of $s$?

Published on 13 Jan 2015 - 13:10

score 61 · Answer 4 · 2015-01-13 21:01:10

61

Views

How can one show that $\prod_{n<p\leq2n}p\leq C(2n,n)$?

Published on 13 Jan 2015 - 21:01

score 196 · Answer 5 · 2026-03-31 13:41:19

196

Views

Hardy-Ramanujan theorem's "purely elementary reasoning"

Published on 31 Mar 2026 - 13:41

score 250 · Answer 6 · 2015-01-16 10:12:38

250

Views

Is $\sum\frac1{p^{1+ 1/p}}$ divergent?

Published on 16 Jan 2015 - 10:12

score 460 · Answer 7 · 2015-01-16 20:07:59

460

Views

What is the value of $\sum_{p\le x} 1/p^2$?

Published on 16 Jan 2015 - 20:07

score 315 · Answer 8 · 2015-01-16 22:56:47

315

Views

Is there a monotonic $f$ such that $\sum f(n)$ diverges but $\sum f(p)$ converges?

Published on 16 Jan 2015 - 22:56

score 312 · Answer 9 · 2015-01-19 15:39:33

312

Views

How to calculate this sum like Gauss sum.

Published on 19 Jan 2015 - 15:39

score 830 · Answer 10 · 2015-01-21 18:01:04

830

Views

On the proof of Fejér-Riesz theorem

Published on 21 Jan 2015 - 18:01

score 2.3k · Answer 11 · 2015-01-23 15:00:09

2.3k

Views

What is the inverse of the divisor sum function $\sigma $?

Published on 23 Jan 2015 - 15:00

score 165 · Answer 12 · 2026-03-29 15:16:02

165

Views

Moving the integral $Q(x) = -\frac{e^{-1/2x}}{4i}\int_{1/2-i\infty}^{1/2+i\infty} \zeta(s)\Gamma(\frac{s}{2})\pi^{-s/2}e^{xs} ds$ past Re(s) = 1.

Published on 29 Mar 2026 - 15:16

score 2.1k · Answer 13 · 2026-04-08 05:42:09

2.1k

Views

Explicit formula for floor(x)?

Published on 08 Apr 2026 - 5:42

score 230 · Answer 14 · 2015-01-23 23:37:33

230

Views

Any formula for the exact number of primes below a given bound?

Published on 23 Jan 2015 - 23:37

score 192 · Answer 15 · 2015-01-24 07:47:12

192

Views

Asymptotics of $\sum_{n\leq x}\tau_{k}\left(n\right)$

Published on 24 Jan 2015 - 7:47

List Question

Find the integral values for which $\left(\pi(x+y)\right)^2=4\pi(x)\pi(y)$

Number of the positive integers up to $\sqrt x $ generated by the prime factors of $x$.

Is the integral $\int_1^{\infty} {A(t)}{t^{-s-1}}dt$ a holomorphic function of $s$?

How can one show that $\prod_{n<p\leq2n}p\leq C(2n,n)$?

Hardy-Ramanujan theorem's "purely elementary reasoning"

Is $\sum\frac1{p^{1+ 1/p}}$ divergent?

What is the value of $\sum_{p\le x} 1/p^2$?

Is there a monotonic $f$ such that $\sum f(n)$ diverges but $\sum f(p)$ converges?

How to calculate this sum like Gauss sum.

On the proof of Fejér-Riesz theorem

What is the inverse of the divisor sum function $\sigma $?

Moving the integral $Q(x) = -\frac{e^{-1/2x}}{4i}\int_{1/2-i\infty}^{1/2+i\infty} \zeta(s)\Gamma(\frac{s}{2})\pi^{-s/2}e^{xs} ds$ past Re(s) = 1.

Explicit formula for floor(x)?

Any formula for the exact number of primes below a given bound?

Asymptotics of $\sum_{n\leq x}\tau_{k}\left(n\right)$

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