Erdos-Turan Conjecture.

[wildrabbitt]

Hi,

this post concerns this page :

http://www.mersenneforum.org/attachm...1&d=1442321644


It clearly states that the conjecture has been proven for arithmetic progressions of length 3.

It's from the book this link goes to http://www.springer.com/us/book/9780387953205

published in 2003.

The proof by Roth is on this linked to on this page :

http://arxiv.org/abs/1011.0104

Now the reason for all this is that I'm trying to work out whether or not the wikipedia is out of touch or not because this
page

https://en.wikipedia.org/wiki/Erd%C5...c_progressions

as it is today 15/09/15, sayd that even the case for arithmetic progressions of length 3 is open, which (for the less perspicacious,

is contrary to what the former documents say.

I spent a long time trying to solve the Erdos-Turan conjecture and now I've bought that book, I think I was proabably mislead by the wikipedia about whether or not it's been solved.

Can anyone help?

[R.D. Silverman]

Originally Posted by wildrabbitt

Hi,

this post concerns this page :

http://www.mersenneforum.org/attachm...1&d=1442321644


It clearly states that the conjecture has been proven for arithmetic progressions of length 3.


I spent a long time trying to solve the Erdos-Turan conjecture

ROTFLMAO.

Hint: Szemeredi's Theorem

and now I've bought that book, I think I was proabably mislead by the wikipedia about whether or not it's been solved.

Can anyone help?

[Batalov]

Originally Posted by wildrabbitt

... mislead by the wikipedia ...

Wikipedia is not a source for any professional study.
Even in high schools almost every teacher drives this point home for every student by all means possible to them.

[wildrabbitt]

ROTFLMAO.

Hint: Szemeredi's Theorem

I've read the page on the wikipedia again and because it says this :

In 1936, Erdős and Turán made the weaker conjecture that any set of integers with positive natural density contains infinitely many 3 term arithmetic progressions.[1] This was proven by Klaus Roth in 1952, and generalized to arbitrarily long arithmetic progressions by Szemerédi in 1975 in what is now known as Szemerédi's theorem.


I'm starting to think that the page I posted from Paul Erdos' book is in fact nothing to do with the Erdos-Turan Conjecture but is about the different conjecture made in 1936.

So I'm inclined to believe the wikipedia in this instance is correct.


Now I realise I proabably deserve a few tomatoes in the face for my behaviour on my 'probabilistic number theory' thread but I'd like
to say thanks for the replies here.
I can see to that someone has replied on this thread before I've posted this so if it seems unfluent please forgive me.

[LaurV]

No tomato from me. When I don't know the subject, I still click on links and try to read and understand, if the time allows me to do so, and I always prefer a math subject instead of politics, etc, at least, this is a math-related forum... So, I clicked the links, read a bit around, partially understood, and felt happy and thank you and the people who participated. No tomato.