Question

$\lim\limits_{n \to \infty}\frac {\log(n)}{\log(p_{n})}=1 $ where $p_{n}$ denotes the nth prime

score 79 · Answer 1 · 2026-04-16 03:02:09

79

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$\lim\limits_{n \to \infty}\frac {\log(n)}{\log(p_{n})}=1 $ where $p_{n}$ denotes the nth prime

Published on 16 Apr 2026 - 3:02

score 141 · Answer 2 · 2026-04-14 18:26:18

141

Views

How can we prove $\sum_{p\leq x}\ln(p) < 2x$?

Published on 14 Apr 2026 - 18:26

score 163 · Answer 3 · 2026-04-14 18:08:31

163

Views

Finding the value of $\sum_{c|n}\mu(c)\log^2(\frac n c)$

Published on 14 Apr 2026 - 18:08

score 379 · Answer 4 · 2026-04-14 16:41:35

379

Views

Lower bound for sum of reciprocal of primes

Published on 14 Apr 2026 - 16:41

score 117 · Answer 5 · 2026-04-15 21:57:35

117

Views

$\sum_{n>x}\frac{\mu^{2}(n)}{n\varphi(n)}=\mathcal{O}(\frac{1}{x})$

Published on 15 Apr 2026 - 21:57

score 74 · Answer 6 · 2026-04-11 17:49:10

74

Views

Why does does one of the core theorems in the Selberg-Delange theorem have useless error bounds?

Published on 11 Apr 2026 - 17:49

score 307 · Answer 7 · 2026-04-11 14:24:11

307

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Deriving The Symmetry Formula of Selberg (Prime Number Theorem)

Published on 11 Apr 2026 - 14:24

score 97 · Answer 8 · 2026-04-16 12:32:36

97

Views

Relation between $(q^4;q^4)_\infty$ and $(q;q)^4_\infty$

Published on 16 Apr 2026 - 12:32

score 62 · Answer 9 · 2026-03-25 22:24:52

62

Views

An $L-$function and a $J-$function. Related?

Published on 25 Mar 2026 - 22:24

score 160 · Answer 10 · 2026-04-15 05:57:16

160

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Which book has the proof of $\sum_{n \leq x}\log^h(\frac x n)= O(x)$?

Published on 15 Apr 2026 - 5:57

score 116 · Answer 11 · 2026-04-16 07:01:04

116

Views

$\sum_{\Im(\rho)>0}\frac{1}{\mid{\rho-\frac{1}{2}}\mid^2}\ll \int_{1}^{\infty} \frac{d(t\log t)}{t^2}$.

Published on 16 Apr 2026 - 7:01

score 226 · Answer 12 · 2026-04-14 21:16:24

226

Views

Establish an upper bound for $\zeta'(s)\over\zeta(s)$?

Published on 14 Apr 2026 - 21:16

score 123 · Answer 13 · 2026-04-13 06:50:31

123

Views

Higher power of logarithms connected to Robin and Nicolas inequalities

Published on 13 Apr 2026 - 6:50

score 125 · Answer 14 · 2026-04-11 22:21:40

125

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Implying form the Symmetry of the sum of von Mangoldt function

Published on 11 Apr 2026 - 22:21

score 208 · Answer 15 · 2026-04-14 10:28:15

208

Views

Silverman Rational Points on Elliptic Curves Exercise 4.3c: Counting points on the Fermat curve over mod p

Published on 14 Apr 2026 - 10:28

List Question

$\lim\limits_{n \to \infty}\frac {\log(n)}{\log(p_{n})}=1 $ where $p_{n}$ denotes the nth prime

How can we prove $\sum_{p\leq x}\ln(p) < 2x$?

Finding the value of $\sum_{c|n}\mu(c)\log^2(\frac n c)$

Lower bound for sum of reciprocal of primes

$\sum_{n>x}\frac{\mu^{2}(n)}{n\varphi(n)}=\mathcal{O}(\frac{1}{x})$

Why does does one of the core theorems in the Selberg-Delange theorem have useless error bounds?

Deriving The Symmetry Formula of Selberg (Prime Number Theorem)

Relation between $(q^4;q^4)_\infty$ and $(q;q)^4_\infty$

An $L-$function and a $J-$function. Related?

Which book has the proof of $\sum_{n \leq x}\log^h(\frac x n)= O(x)$?

$\sum_{\Im(\rho)>0}\frac{1}{\mid{\rho-\frac{1}{2}}\mid^2}\ll \int_{1}^{\infty} \frac{d(t\log t)}{t^2}$.

Establish an upper bound for $\zeta'(s)\over\zeta(s)$?

Higher power of logarithms connected to Robin and Nicolas inequalities

Implying form the Symmetry of the sum of von Mangoldt function

Silverman Rational Points on Elliptic Curves Exercise 4.3c: Counting points on the Fermat curve over mod p

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