Question

Some convincing reasoning to show that to prove that Ramanujan tau function is multiplicative is very difficult

score 1.2k · Answer 1 · 2026-03-23 06:31:40

1.2k

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Some convincing reasoning to show that to prove that Ramanujan tau function is multiplicative is very difficult

Published on 23 Mar 2026 - 6:31

score 878 · Answer 2 · 2026-03-25 09:31:45

878

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Integrating a function over a vertical line in the complex plane

Published on 25 Mar 2026 - 9:31

score 147 · Answer 3 · 2018-02-20 14:30:01

147

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Evaluate a Dirichlet series related to the ring of Gaussian integers

Published on 20 Feb 2018 - 14:30

score 89 · Answer 4 · 2026-03-27 23:00:23

89

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Justify an approximation of $-\sum_{n=2}^\infty H_n\left(\frac{1}{\zeta(n)}-1\right)$, where $H_n$ denotes the $n$th harmonic number

Published on 27 Mar 2026 - 23:00

score 106 · Answer 5 · 2026-03-26 08:02:17

106

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$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

Published on 26 Mar 2026 - 8:02

score 225 · Answer 6 · 2026-03-22 14:40:38

225

Views

$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

Published on 22 Mar 2026 - 14:40

score 199 · Answer 7 · 2026-03-27 10:34:19

199

Views

Show $\zeta(s)$ doesn't have a zero on interval $[0, 1]$

Published on 27 Mar 2026 - 10:34

score 118 · Answer 8 · 2026-03-25 04:10:44

118

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The asymptotic of $\sum_{1\leq n\leq x}\frac{\sum_{k\leq n}\mu(k)}{n\cdot\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$ versus conjectures

Published on 25 Mar 2026 - 4:10

score 120 · Answer 9 · 2026-03-25 12:35:05

120

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Justify an approximation of $\sum_{n=1}^\infty G_n\zeta(n+1)$, where $G_m$ denotes the so-called Gregory coefficients

Published on 25 Mar 2026 - 12:35

score 143 · Answer 10 · 2026-03-22 17:06:59

143

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A conjecture about the asymptotic of the absolute value of $\sum_{k=1}^n\sin\left(N_k\right)$, where $N_k$ is the primorial of order $k$

Published on 22 Mar 2026 - 17:06

score 255 · Answer 11 · 2018-02-25 00:53:47

Showing $\prod\limits_{p \leq x} p> e^{(1+\epsilon )x}$ and $\prod\limits_{p \leq x} p < e^{(1-\epsilon) x}$ are false for $x$ large enough.

score 25 · Answer 12 · 2026-03-25 13:55:20

25

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Analyze a particular example of approximation for $\int_N^M(\sin(\pi(t)))^2dt$, where $\pi(x)$ is the prime-counting function

Published on 25 Mar 2026 - 13:55

score 232 · Answer 13 · 2026-03-25 20:19:47

232

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Ramanujan's $\pi(x)^{2}<{\frac {ex}{\log x}}\pi {\bigg (}{\frac {x}{e}}{\bigg )}$

Published on 25 Mar 2026 - 20:19

score 145 · Answer 14 · 2026-03-25 13:57:54

145

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Let $(a_n)_{n=1}^\infty$ be an infinite sequence of complex numbers. Prove the following limit.

Published on 25 Mar 2026 - 13:57

score 104 · Answer 15 · 2026-03-25 01:21:54

104

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Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

Published on 25 Mar 2026 - 1:21

List Question

Some convincing reasoning to show that to prove that Ramanujan tau function is multiplicative is very difficult

Integrating a function over a vertical line in the complex plane

Evaluate a Dirichlet series related to the ring of Gaussian integers

Justify an approximation of $-\sum_{n=2}^\infty H_n\left(\frac{1}{\zeta(n)}-1\right)$, where $H_n$ denotes the $n$th harmonic number

$\sum_{p\leq n}\sum_{q\leq N}\sum_{n\leq N;p|n,q|n}1=^? \sum_{pq \leq N}\big( \frac N{pq}+O(1)\big)+\sum_{p \leq N}\big( \frac N{p}-\frac N{p^2}\big)$

$Var[w]=O(\log\log(N))$ where $w(n)$ is the no of prime divisors of $n$

Show $\zeta(s)$ doesn't have a zero on interval $[0, 1]$

The asymptotic of $\sum_{1\leq n\leq x}\frac{\sum_{k\leq n}\mu(k)}{n\cdot\operatorname{rad}(n)}\log\left(\frac{x}{n}\right)$ versus conjectures

Justify an approximation of $\sum_{n=1}^\infty G_n\zeta(n+1)$, where $G_m$ denotes the so-called Gregory coefficients

A conjecture about the asymptotic of the absolute value of $\sum_{k=1}^n\sin\left(N_k\right)$, where $N_k$ is the primorial of order $k$

Showing $\prod\limits_{p \leq x} p> e^{(1+\epsilon )x}$ and $\prod\limits_{p \leq x} p < e^{(1-\epsilon) x}$ are false for $x$ large enough.

Analyze a particular example of approximation for $\int_N^M(\sin(\pi(t)))^2dt$, where $\pi(x)$ is the prime-counting function

Ramanujan's $\pi(x)^{2}<{\frac {ex}{\log x}}\pi {\bigg (}{\frac {x}{e}}{\bigg )}$

Let $(a_n)_{n=1}^\infty$ be an infinite sequence of complex numbers. Prove the following limit.

Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer

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