Talk:Birch and Swinnerton-Dyer conjecture

message: Conjecture: If and only if L(C, 1) = 0 then C(Q) is infinite. 128.208.160.222 23:27, 31 May 2006 (UTC)
replies: text: No. Why should it? Charles Matthews 18:47, 16 November 2006 (UTC)
thread_title: Untitled

message: In the section History, the Tate–Shafarevich group is denoted by Sha(E), but the standard notation (see, in particular, the article) for it is Ш. K9re11 (talk) 10:52, 22 October 2014 (UTC)
replies: text: These are almost the same thing. The English spelling of the name of the Cyrillic character Ш is sha. I suspect part of the problem is that the mathematics formatting system used by Wikipedia does not include codes for producing the sha character. —David Eppstein (talk) 17:42, 22 October 2014 (UTC)
thread_title:  Tate–Shafarevich group 

message: The article contains this phrase:
"The conjecture was subsequently extended to include the prediction of the precise leading Taylor coefficient of the L-function at s = 1. It is conjecturally given by",
which is followed by a complicated expression that is conjecturally equal to the coefficient of the first non-zero coefficient of the Taylor expansion of the Hasse-Weil L-function of an elliptic curve E about the number 1.
Why is this conjecture not attributed to anyone (or to any group of people)?
And why is the expression for the value of the aforesaid coefficient only partly described?  Would it be that hard to complete the description of it?  
I hope someone knowledgeable on this topic will fill in the missing information.Daqu (talk) 04:03, 28 January 2015 (UTC)
thread_title:  Whose conjecture is this extension of the Birch and Swinnerton-Dyer conjecture? 

message: Substituted at 01:49, 5 May 2016 (UTC)
thread_title: Assessment comment

message: The Laurel and Hardy comparison stays because it gives analogies on the personal character of two mathematicians which is impossible to get with other means. Compare for example to other mathematical duos: 1) Einstein gregarious, happy, full of laughter and common sense, and Gödel extremely solemn, very serious, quite solitary, and distrustful of common sense 2) If Serre was a Mozart, Grothendieck was a Wagner. This sort of material written by a top mathematician and popular expositor in a published book is encyclopedic and stays. Solomon7968 04:21, 25 November 2016 (UTC)
thread_title:  Laurel and Hardy 

message: Has it been solved recently?
* https://www.livescience.com/deepmind-artificial-intelligence-pure-math
--Ernsts (talk) 13:26, 7 December 2021 (UTC)
thread_title:  News 

message: Some key points:
1. We should show the exact relationship between the order of the zero of L(E, s) and the rank of E rather than making some indirect statements. Like "given by more refined data" seems vague and does not lead to anything.
2. L(E, s) is not even defined, just described that it is "an Euler product" without any mathematical expression.
3. The two forms of the conjecture per Wiles' paper should be stated here as well. SkyFlubbler (talk) 15:35, 22 June 2023 (UTC)
thread_title:  Further elaboration? 

message: https://www.ripublication.com/atam20/atamv15n1_04.pdf Cssenthusiast (talk) 03:19, 8 April 2024 (UTC)
replies: text: That's a predatory journal, unlikely to be the place where a valid solution would be published, and (more to the point for us) unusable as a reliable source here. —David Eppstein (talk) 06:21, 8 April 2024 (UTC)
thread_title:  Did Daniel John Thompson solve it?