Talk:Generalized Riemann hypothesis

"The case &chi;(n) = 1 for all n yields the ordinary Riemann hypothesis."

Such a &chi; is not a Dirichlet character (as there is no positive k s.t. &chi;(n)=0 whenever gcd(n,k)>1). Or am I missing something? -- EJ 14:40, 19 Nov 2004 (UTC)

Try k = 1. Algebraist 20:59, 5 Jun 2005 (UTC)


 * Uhh, yes, thanks. Stupid me. -- EJ 12:51, 11 July 2005 (UTC)

A GRH (disambiguation) page is needed. -Emiellaiendiay 15:23, 5 December 2006 (UTC)

Any competing hypothesis?
Any competing hypothesis which shows any alternative to GRH?

Reddwarf2956 (talk) 19:01, 25 October 2009 (UTC)

Is there anything known about the asymptotics of π(x,a,d), beyond Dirichlet's result, without assuming GRH? It would seem strange to me if there weren't. If there is a known stronger result, then it should be in the article, to give a clearer sense of what improvement GRH would actually yield. I'm not strong in number theory so I wouldn't know the best place to look. -- Spireguy (talk) 01:37, 31 October 2010 (UTC)

Is this a mistake?
If GRH is true, then every proper subgroup of the multiplicative group $$(\mathbb Z/n\mathbb Z)^\times$$ omits a number less than $$2(\ln p)^2\,$$

Seems that $$2(\ln p)^2$$ should be $$2(\ln n)^2$$ — Preceding unsigned comment added by 181.28.138.163 (talk) 17:04, 25 November 2011 (UTC)
 * Fixed.—Emil J. 11:21, 5 April 2012 (UTC)

It now says:
 * If GRH is true, then every proper subgroup of the multiplicative group $$(\mathbb Z/n\mathbb Z)^\times$$ omits a number less than 2(ln n)2, as well as a number coprime to n less than 3(ln n)2.

Isn't the second statement a direct consequence of the first? If I find a number less than 2(ln n)2 it will surely be less than 3(ln n)2. So what's the point here? --Jobu0101 (talk) 10:26, 24 November 2015 (UTC)