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Questions related to the Dirichlet series for $\frac{\zeta'(s)}{\zeta(s)^2}$

score 203 · Answer 1 · 2026-05-10 14:07:38

203

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Questions related to the Dirichlet series for $\frac{\zeta'(s)}{\zeta(s)^2}$

Published on 10 May 2026 - 14:07

score 106 · Answer 2 · 2026-04-16 11:36:16

106

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Equating the coefficients in $\sum_{n=1}^\infty C_{n-1} \frac{t^n}{n!}=\sum_{n=0}^\infty C_n \frac{t^n}{n!} \sum_{m=0}^\infty \frac{t^m}{m!}$

Published on 16 Apr 2026 - 11:36

score 64 · Answer 3 · 2026-05-10 23:31:51

64

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How can we write the expansion of $\frac{e^t(e^t-1)^{n-1}}{(e^t+1)^{n+1}}.$

Published on 10 May 2026 - 23:31

score 751 · Answer 4 · 2026-04-16 19:13:09

751

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Solution to $x^2 \equiv 1$ (mod $pq$), $p,q \geq 3$ primes.

Published on 16 Apr 2026 - 19:13

score 557 · Answer 5 · 2026-04-14 06:50:07

557

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Complex version of the Fermat last problem

Published on 14 Apr 2026 - 6:50

score 63 · Answer 6 · 2026-04-09 17:16:12

63

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Missing in between terms during the process of mathematical induction

Published on 09 Apr 2026 - 17:16

score 1.3k · Answer 7 · 2026-05-10 12:51:56

1.3k

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Evaluating Dirichlet $L$-functions at $s=1$

Published on 10 May 2026 - 12:51

score 58 · Answer 8 · 2026-05-11 04:23:41

58

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What function $f(n)$ is defined by $f(1)=2$ and $f(n+1)=2f(n)$ for $n\geq 1$

Published on 11 May 2026 - 4:23

score 156 · Answer 9 · 2026-04-14 17:07:08

156

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$p$-adic supremum of cyclotomic polynomial

Published on 14 Apr 2026 - 17:07

score 32 · Answer 10 · 2026-04-14 06:21:32

32

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If $c | m_i$ Prove that $c| \sum_{i=1}^r u_i m_i$ where $m_i,u_i,c \in \mathbb{Z}$ and $i=1,2,..,r$

Published on 14 Apr 2026 - 6:21

score 155 · Answer 11 · 2026-04-15 04:14:22

155

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Arbitrarily large sequence of numbers with a property

Published on 15 Apr 2026 - 4:14

score 152 · Answer 12 · 2026-04-15 19:01:34

152

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Find the smallest positive integer $\ell$ such that $3 \cdot \left(4^m + 1\right)$ divides $2^\ell-1$

Published on 15 Apr 2026 - 19:01

score 368 · Answer 13 · 2026-04-14 15:06:37

368

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irreducibility of $(\zeta + \zeta ^{-1})$'s minimal polynomial over $\mathbb{Z}[x]$

Published on 14 Apr 2026 - 15:06

score 70 · Answer 14 · 2026-05-11 00:47:05

70

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Writing down consecutive natural numbers until a certain number of digits $k$ is reached.

Published on 11 May 2026 - 0:47

score 32 · Answer 15 · 2026-04-14 05:06:00

32

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How to solve for these two values - square root modulo composite and Chinese remainder theorem

Published on 14 Apr 2026 - 5:06

List Question

Questions related to the Dirichlet series for $\frac{\zeta'(s)}{\zeta(s)^2}$

Equating the coefficients in $\sum_{n=1}^\infty C_{n-1} \frac{t^n}{n!}=\sum_{n=0}^\infty C_n \frac{t^n}{n!} \sum_{m=0}^\infty \frac{t^m}{m!}$

How can we write the expansion of $\frac{e^t(e^t-1)^{n-1}}{(e^t+1)^{n+1}}.$

Solution to $x^2 \equiv 1$ (mod $pq$), $p,q \geq 3$ primes.

Complex version of the Fermat last problem

Missing in between terms during the process of mathematical induction

Evaluating Dirichlet $L$-functions at $s=1$

What function $f(n)$ is defined by $f(1)=2$ and $f(n+1)=2f(n)$ for $n\geq 1$

$p$-adic supremum of cyclotomic polynomial

If $c | m_i$ Prove that $c| \sum_{i=1}^r u_i m_i$ where $m_i,u_i,c \in \mathbb{Z}$ and $i=1,2,..,r$

Arbitrarily large sequence of numbers with a property

Find the smallest positive integer $\ell$ such that $3 \cdot \left(4^m + 1\right)$ divides $2^\ell-1$

irreducibility of $(\zeta + \zeta ^{-1})$'s minimal polynomial over $\mathbb{Z}[x]$

Writing down consecutive natural numbers until a certain number of digits $k$ is reached.

How to solve for these two values - square root modulo composite and Chinese remainder theorem

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