One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity.

#黒 #猫耳付き #パーカー #青年 #人形 #AI #けんきさん #kenki #ZETA DIVISION

みてみて　www　K-popアイドル風けんき君さん！！！　なり。('ω')ぷくり。ｗ

Episódio 161 – Be, BeBox e BeOS – Parte B

https://retropolis.com.br/2025/03/19/episodio-161-parte-b/

Finally managed to run #zed on #nixos with local #zeta LLM for recommendations. I only needed to enable #ollama and point zed's settigns to it, nix's ollama configuration even takes care of downloading the models.

https://github.com/woile/nix-config/blob/main/hosts/nixos/configuration.nix#L148-L154

#ZedEditor が新たに #Zeta っていう #AI を Beta リリースしたのか？

https://zed.dev/edit-prediction

Zeta is hiring a Data Engineer II
Location: Bangalore, India

#DataScience #DataScientist #tech #JobSearch #GetFediHired #HashyJobs # #Zeta

https://datasciencejobs.com/jobs/data-engineer-ii-zeta-india-2/

#call4reading

Absolute #Zeta functions and #periodicity of #quantumwalks on cycles #by Jiro Akahori, Norio Konno, Iwao Sato, and Yuma Tamura

https://doi.org/10.26421/QIC24.11-12-1

Zeta is hiring a Data Scientist - I
Location: Bangalore, Karnataka, India

#DataScience #DataScientist #tech #JobSearch #GetFediHired #HashyJobs # #Zeta

https://datasciencejobs.com/jobs/data-scientist-i-zeta-india-1/

#call4reading

Absolute #Zeta fountions for Zeta functions of #quantum cellular automata #by Jiro Akahori, Norio Konno, and Iwao Sato

https://doi.org/10.26421/QIC23.15-16-1 (#arXiv:2307.07106)

Finally managed to get #zeta-c working on the #LispM!

#Zeta-C progress. #LispM #LispMachine revoöution

#Zeta-C almost working again after 40 years. #LispM #LispMachine

Currently on my first long-distance travel in a very long time and it does feel very special and exciting. The destination, South #Korea, is certainly a key factor!

And the program is packed, with four events – and associated dinners ;-) – in the next four days.

So cool to be speaking about our work in #CLS from several projects at @tcdh, including on #Zeta, #MiMoText, #ELTeC and @CLSinfra. I'm also very eager to learn more about Korean DH research!

Details: https://christof-schoech.de/activities/?_sf_s=Korea

Interesting integral! #Challenge
$${\displaystyle {\int }_0^1{\displaystyle \frac{\ln (x)\ln (1-x)}{x(1-x)}}{\mathrm{Li}}_2(x)dx=5\zeta (2)\zeta (3)-8\zeta (5)}$$
Where ${\mathrm{Li}}_2(x)$ denotes the dilogarithm (or Spence's function), and $\zeta (x)$ denotes the Riemann zeta function.

A representation of $18$ using an analytic continuation of the Dirichlet series and the numbers $0,1,2,3,4,5,6$.
$$18=\left|{\displaystyle \frac{1}{{\zeta }^2(0)}}({\displaystyle \frac{\mathcal{H}(-6)}{\zeta (-5)}}-{\displaystyle \frac{\mathcal{H}(-2)}{\zeta (-1)}}){\displaystyle \frac{\mathcal{H}(-4)}{\zeta (-3)}}\right|$$
where ${\displaystyle \zeta (z)=\sum _{n\ge 1}{\displaystyle \frac{1}{n^z}}}$ denotes the Riemann zeta function, and ${\displaystyle \mathcal{H}(z)=\sum _{n\ge 1}{\displaystyle \frac{H_n}{n^z}}}$ denotes the harmonic zeta function.

Power series for the cotangent and cosecant functions can be expressed rather compactly in terms of the Riemann zeta and Dirichlet eta functions:

$${\displaystyle \cot z=-2\sum _{k=0}^{\mathrm{\infty }}\frac{\zeta (2k)}{{\pi }^{2k}}{z}^{2k-1}\csc z=2\sum _{k=0}^{\mathrm{\infty }}\frac{\eta (2k)}{{\pi }^{2k}}{z}^{2k-1}}$$

Since I haven't seen these expressed quite this way before, I thought I'd share it. More information is available here:

https://analyticphysics.com/Special%20Functions/Zeta%20Functions%20in%20Trigonometry.htm

The unproved Riemann hypothesis states that the nontrivial zeros of the Riemann zeta function occur only on the critical line $z=\frac{1}{2}+iy$. While it is not difficult to understand why these zeros can only occur inside the critical strip $0<\mathrm{Re}z<1$, the restriction to the critical line is spooky cool.

With an implementation of the zeta function in #JavaScript one has a proof near the origin via #visualization. The real part of the function is blue, imaginary red:

https://mathcell.org/www/riemann-zeta-zeros.htm

Manipulating the imaginary part of the argument along the critical strip shows immediately that zeros only occur on the critical line for an imaginary part of approximately

±14.13, ±21.02, ±25.01, ±30.42, ±32.94, ±37.59, ±40.92, ±43.33, ±48.01, ±49.77

For more context and the relation to the Riemann xi function, visit

https://analyticphysics.com/Special%20Functions/Visualizing%20Riemann%20Zeta%20Function%20Zeros.htm

#NowPlaying on #KEXP's #LiveOnKEXP

Zeta:
La Flor De La Palabra

#Zeta

https://open.spotify.com/track/39ACAuJdQJd7gtlKWCOl6Z

https://joinzeta.bandcamp.com/track/la-flor-de-la-palabra

#KEXP #playlist
https://open.spotify.com/playlist/6VNALrOa3gWbk794YuIrwg

On the ζ ring of ⛢

https://arxiv.org/abs/2305.07190