Talk:Heegner number

message: What does the function denoted Q in this article refer to?
:Quadratic Field
No, rational numbers. Charles Matthews 20:57, 12 Mar 2004 (UTC)
replies: text: No, "ring of integers" is correct. See this article. An ""ideal" is a subset of a ring that is closed under addition, with the additional property that if any element in the ideal is multiplied by a ring element, the result still lies in the ideal. If we consider the ring of ordinary integers, then if n is any integer the set {..., −3n, −2n, −n, 0, n, 2n, 3n, ...} is an ideal because (a) it's closed under addition, and (b) if we multiply any multiple of n by an integer we obtain another multiple of n. (The concept of an ideal grew out of a desire to understand different sorts of algebraic numbers, where addition and multiplication aren't necessarily tied together the way they are in the natural numbers.)  DavidCBryant 19:34, 8 January 2007 (UTC)

message: I read today a recent post on sci.math.research by Titus P. on the additional structure of the integers obtained as exp(pi sqrt n), namely e^(pi sqrt n) - 744 = (12(a(n)^2-1))^3, where the a(n) are consequently extremely close to an integer for Heegner numbers (=3 mod 4).
Could somebody sufficiently competent add one or 2 phrases (and/or xrefs) about that? — MFH:Talk 03:53, 16 April 2008 (UTC)
thread_title:  structure of the J(...)=x^3 term 

message: Does anyone know why e^{\pi \sqrt{58}} is so close to an integer? 4 T C 07:54, 8 January 2010 (UTC)
thread_title: ?

message: Can someone give an exact reference to the fact that this was conjectured by Gauss?
Gauss' class number one list, row I.1 in article 303 of Disquisitiones Arithmeticae, is: 1,2,3,4,7
and the completeness of this list was proved by Landau 1902 (see Goldfeld, Bull. AMS, 1985, p.26). 
Gauss is looking at a slightly different question, with nontrivial overlap, but different. Did he conjecture _elsewhere_ this 
Heegner list? 
129.199.2.17 (talk) 09:20, 26 October 2012 (UTC)
replies: text: I don't know off-hand the answer to your question, but the point is that Gauss conjectured something which in modern terms is that those nine numbers give all imaginary quadratic fields of class number 1. It is very common in math to restate conjectures/theorems like this and still attribute them to the old folks. RobHar (talk) 07:16, 27 October 2012 (UTC)
thread_title:  was this really conjectured by Gauss? 

message: So reads a hidden comment throughout the article.  I wonder whether there is any reason not to.  I can only suppose that it's because something like e^{\pi \sqrt{163}} = 262,537,412,640,768,743.99999999999925...  won't work but e^{\pi \sqrt{163}} = 262{,}537{,}412{,}640{,}768{,}743.99999999999925...  does and is used on the article.  Better still, though, we could have e^{\pi \sqrt{163}} = 262\,537\,412\,640\,768\,743.999\,999\,999\,999\,25...  as in this version.  The article is much more readable when numbers are formatted.  Can anyone enlighten me as to whether there is some convention not to format numbers within <math> and why this would be so given that all <math> is is a tool for displaying formulae etc.? Jimp 13:10, 19 April 2015 (UTC)
thread_title:  don't put thousands separators under <nowiki><math></nowiki>! 

message: I fixed the formatting in 
→‎Almost integers and Ramanujan's constant: 
with the explanation 
had bad formatting of the compound exponential, as easily shown by actually computing the number. As previously shown, including on MathWorld (still in error), the final exponentiation was improperly shown as mere multiplication. I have corrected the formatting for both the wiki article itself and the equation from the references. The latter correction may be improper, but it seems best to stop propagating the error. Someone tell me! YodaWhat (talk) 09:20, 25 February 2020 (UTC)
replies: text: Your changes were wrong and have been reverted. Exponentiation is right-associative (see Exponentiation#Identities and properties), so abc means a(bc) which is not the same as (ab)c. You may also be unaware of the rule (ab)c = ab×c. The expressions could have been written as (ab)c with the parentheses but it's far more common to write ab×c. PrimeHunter (talk) 20:06, 7 March 2020 (UTC)

text: As I said, exponentiation is right-associative. This is a mathematical definition. See e.g. the Google search . Don't trust some old calculator. It's harder to implement right-associative and many calculators don't do it. Modern programming languages usually follow the mathematical definition. See e.g. https://www.wolframalpha.com/input/?i=2%5E2%5E3, or enter 2^2^3 at https://pari.math.u-bordeaux.fr/gp.html. They both compute 2^2^3 = 2^(2^3) = 2^8 = 256, whereas (2^2)^3 = 64. Anyway, the article never says abc so we don't even have to discuss the correct meaning unless you change the article to use that notation incorrectly. It's not an insult to simply say that somebody is wrong. You are however insulting me, and you are still wrong. Please see Wikipedia:No personal attacks and Wikipedia:Civility. By the way, it wasn't me who reverted you, but I agree with the user who did it. The article is correct and MathWorld is correct. e^{\pi \sqrt{163}} only has one exponentiation since π and 163 has the same baseline in the typography. The expression is e^{(\pi \times \sqrt{163})} by syntactic definition, without even having to define exponentiation. PrimeHunter (talk) 23:43, 2 May 2020 (UTC)
thread_title:  Bad formatting of the compound exponentials appears to be a problem throughout this entire wiki article. I fixed one section. Expert Review Needed!