Question

Two questions concerning series involving the Möbius function and trigonometric functions

score 47 · Answer 1 · 2026-05-02 20:08:43

47

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Two questions concerning series involving the Möbius function and trigonometric functions

Published on 02 May 2026 - 20:08

score 115 · Answer 2 · 2026-05-10 19:19:48

115

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Two miscellaneous questions about equations involving the Euler's totient function and twin primes

Published on 10 May 2026 - 19:19

score 55 · Answer 3 · 2026-05-03 13:16:42

$\left[\frac{\log( \log x / \log 2 )}{\log 2} \right] \ge \frac{\log_2 x}{\log 2}- \left( 1 + \frac{1}{\log 2} \right)$

score 63 · Answer 4 · 2026-05-03 13:18:47

63

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Is there any intuition behind why $\zeta(-1) = \int_{-1}^{0} \frac{N(N+1)}{2}$?

Published on 03 May 2026 - 13:18

score 127 · Answer 5 · 2026-05-03 13:18:47

127

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Convergence of the series $\sum_{n=1}^{\infty}\frac{1}{4^{\omega(n)}n}$

Published on 03 May 2026 - 13:18

score 71 · Answer 6 · 2026-05-06 17:59:02

71

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ideas on how to prove this statement about the Gram points?

Published on 06 May 2026 - 17:59

score 188 · Answer 7 · 2026-05-12 04:33:56

188

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A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

Published on 12 May 2026 - 4:33

score 63 · Answer 8 · 2026-05-10 19:40:36

63

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On primes of the form $2\pi(n)p_n+1$, for some $n\geq 1$ being $\pi(x)$ the prime-counting function and $p_k$ the $k$th prime number

Published on 10 May 2026 - 19:40

score 229 · Answer 9 · 2026-05-12 01:41:48

229

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I have a proof concerning prime numbers. Should I publish my result?

Published on 12 May 2026 - 1:41

score 1.1k · Answer 10 · 2026-04-29 12:41:07

1.1k

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Existence of totally real number fields of any degree

Published on 29 Apr 2026 - 12:41

score 116 · Answer 11 · 2026-03-29 07:33:43

116

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Why is $\sum_{j^2\leq \sqrt x} \mu(j)[\frac x {j^2}]=x\sum_{j^2\leq \sqrt x}\frac {\mu(j)} {j^2}+ O(\sqrt x)$?

Published on 29 Mar 2026 - 7:33

score 980 · Answer 12 · 2026-05-13 01:52:14

980

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What are the different subjects in number theory to do research?

Published on 13 May 2026 - 1:52

score 94 · Answer 13 · 2026-05-03 13:18:53

94

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Let $A(x) = \sum_{n\leq x} a(n)$, is it possible that $A(x) = π(x) + O(\sqrt x)$

Published on 03 May 2026 - 13:18

score 70 · Answer 14 · 2026-05-10 13:29:26

70

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Why is $\prod\limits_{p\le Y}\left(1+\frac{1+2e}{p}\right)\le(\log Y)^{10}$

Published on 10 May 2026 - 13:29

score 125 · Answer 15 · 2026-05-10 16:03:31

125

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Where is positive or negative the function $\sum_{n=1}^\infty\frac{\mu(n)}{n}\left(\frac{\cos(nx)}{n}\right)^2$ over the set $[0,2\pi]$?

Published on 10 May 2026 - 16:03

List Question

Two questions concerning series involving the Möbius function and trigonometric functions

Two miscellaneous questions about equations involving the Euler's totient function and twin primes

$\left[\frac{\log( \log x / \log 2 )}{\log 2} \right] \ge \frac{\log_2 x}{\log 2}- \left( 1 + \frac{1}{\log 2} \right)$

Is there any intuition behind why $\zeta(-1) = \int_{-1}^{0} \frac{N(N+1)}{2}$?

Convergence of the series $\sum_{n=1}^{\infty}\frac{1}{4^{\omega(n)}n}$

ideas on how to prove this statement about the Gram points?

A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions

On primes of the form $2\pi(n)p_n+1$, for some $n\geq 1$ being $\pi(x)$ the prime-counting function and $p_k$ the $k$th prime number

I have a proof concerning prime numbers. Should I publish my result?

Existence of totally real number fields of any degree

Why is $\sum_{j^2\leq \sqrt x} \mu(j)[\frac x {j^2}]=x\sum_{j^2\leq \sqrt x}\frac {\mu(j)} {j^2}+ O(\sqrt x)$?

What are the different subjects in number theory to do research?

Let $A(x) = \sum_{n\leq x} a(n)$, is it possible that $A(x) = π(x) + O(\sqrt x)$

Why is $\prod\limits_{p\le Y}\left(1+\frac{1+2e}{p}\right)\le(\log Y)^{10}$

Where is positive or negative the function $\sum_{n=1}^\infty\frac{\mu(n)}{n}\left(\frac{\cos(nx)}{n}\right)^2$ over the set $[0,2\pi]$?

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