Timeline for Nick Katz observation: "the rationality of the zeta function!"
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jun 29, 2018 at 15:43 | comment | added | efs | Thanks @WillSawin. I'm aware now that Iwasawa was kind of searching "similarities" between number fields and function fields over finite fields. I hope to understand this better one day. Thanks again. | |
| Jun 29, 2018 at 5:50 | comment | added | Will Sawin | It's important to note that Iwasawa's construction of the $p$-adic zeta function was inspired partially by Weil's construction of function field zeta functions, which are rational. So ACL is not quite right to say that this is quite unrelated to the Weil conjectures - while there is no formal relation, they can be described in similar ways. | |
| Jun 24, 2017 at 16:14 | comment | added | efs | @ACL. I searched "weil conjectures" and "p-adic zeta" in MR, and found nothing. I was just hoping for some interesting relation :) | |
| Jun 24, 2017 at 16:12 | history | edited | efs | CC BY-SA 3.0 |
added 271 characters in body
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| Jun 23, 2017 at 18:43 | comment | added | ACL | The exclamation point makes me think it is an act of humor: the algebraic gadget describing the p-adic zeta function "is" a rational function. This reminds of the Weil conjecture, of course, but is quite unrelated. | |
| Jun 23, 2017 at 17:34 | comment | added | efs | @ Matt F. In the article, Katz writes this with the exclamation point. I am quoting it verbatim. | |
| Jun 23, 2017 at 17:31 | comment | added | user44143 | Gratuitous exclamation points encourage downvotes. | |
| Jun 23, 2017 at 16:59 | comment | added | efs | Ok. This seems clear now. It was a simple observation about Iwasawa's construcion of $p$-adic $L$-series. Thank you very much. (Sometimes, Katz papers are extremely hard to read, since he seems to understand everything in great generality.) | |
| Jun 23, 2017 at 16:53 | comment | added | js21 | Here I would understand "rational" in the sense that the Iwasawa transform of $\mu^{(a)}$ is rational (as a power series). | |
| Jun 23, 2017 at 16:50 | comment | added | efs | Rationality in the sense of "rational values at negative integers"? | |
| Jun 23, 2017 at 16:47 | comment | added | js21 | I took a look at this article by Katz, and it seems to me that he is referring to Riemann's zeta function (whence the exclamation mark). | |
| Jun 23, 2017 at 16:35 | comment | added | efs | Ok, I understand. But maybe one should explain the reason. Sometimes I see downvotes in questions that after a while become excelent ones, with a lot of upvotes and feedback. | |
| Jun 23, 2017 at 16:32 | comment | added | js21 | EFinat-S : to answer your question about "User"'s question (now deleted by the poster) on Riemann's zeta function, it was probably downvoted because his/her question did not make any sense... | |
| Jun 23, 2017 at 15:55 | history | asked | efs | CC BY-SA 3.0 |