Talk:Generalized Riemann hypothesis
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"The case χ(n) = 1 for all n yields the ordinary Riemann hypothesis."
Such a χ is not a Dirichlet character (as there is no positive k s.t. χ(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)
Any competing hypothesis?
Any competing hypothesis which shows any alternative to GRH?
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 omits a number less than
It now says:
- If GRH is true, then every proper subgroup of the multiplicative group 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)