Talk:Mertens conjecture

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Who did the search for counterexamples up to 10^14 and is the result published somewhere? (Akruppa)

There is an interesting discussion of the Mertens conjecture in Talk:Möbius_function. Perhaps some of that material could be moved here.


Cleanup:

Dates for S. are inconsistent. Also RH has not been proven false. This page is inaccurate.

  • the article does not claim that RH has been proven false. Read more carefully.
  • what exactly, precisely is inconsistent with S. dates ?

--FvdP 17:51, 14 Jan 2005 (UTC)

Contents

[edit] Tag for context

I have tagged the article to be cleanup for context. Right now, it is very hard for readers without high level of math background to get a sense of what this is about. Perhaps give a 1 paragraph summary for the layman as introduction in the beginning of the article??

[edit] Is the first Sigma missing the upper bound of summation?

It just appears as though there is nothing there. Is this a mistake, or is there something that I'm not understanding about its context in the article? --Ķĩřβȳ♥ŤįɱéØ 07:46, 14 August 2006 (UTC)

[edit] No more a conjecture

A conjecture is an open question. And this one is closed. Not a conjecture. High time to create a new category. 83.199.53.61 22:30, 1 November 2006 (UTC)

[edit] Bounds on counter examples

There seems to be disagreement about the upper bound 3.21*10^64 [1] or exp(3.21*10^64) [2]. Does somebody have access to a peer reviewed paper? (Not just claims about what such a paper says) Where is the lower bound 10^14, and upper bound 1.59*10^40 or exp(1.59×10^40) from? PrimeHunter 23:49, 31 January 2007 (UTC)

MathWorld is wrong. Read "Further systematic computations on the summatory function of the Möbius function" by Kotnik and van de Lune. They refer to Pintz for the exp(3.21*10^64) bound. 10^40 was to good to be true :-) // Wellparp 08:13, 1 February 2007 (UTC)
See also this talk by te Riele [www.math.tu-berlin.de/~kant/ants/Proceedings/te_riele/te_riele_talk.pdf] // Wellparp 08:17, 1 February 2007 (UTC)
Thanks for the link which confirms the 3 bounds the article mentions. I have added the link in the references. PrimeHunter 13:44, 1 February 2007 (UTC)

[edit] The integral after the Mellin Inversion Theorem is wrong

The integral after the application of the Mellin Inversion Theorem seems wrong.

The integral is from "sigma-is" to "sigma+is", but the term inside the integral is of the form f(s)ds. Presumably this should be sigma-ix and sigma+ix?

Thomaso (talk) 16:48, 2 January 2008 (UTC)

Note that x also appears under integral. I think the integral should be taken over the line \Re s = \sigma (i.e. from \sigma - i \infty to \sigma + i \infty).
83.6.63.59 (talk) 22:24, 7 February 2008 (UTC)