Talk:Erdős conjecture on arithmetic progressions

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Was Turán a coconjecturer? I don't see any reference that mentions his name specifically in connection with this problem. For example, Bollobás attributes the conjecture to Erdős and only him in Paul Erdős—Life and work, in: The Mathematics of Paul Erdős, I, Springer, p. 40. Erdős himself writes "In this connection I conjecture that if \sum^{\infty}_{r=1}\frac{1}{a_r}=\infty then for every k there are k ar's in an arithmetic progression." P. Erdős: On the combinatorial problems which I would most like to see solved, Combinatorica, '1(1981), 28.Kope 06:57, 16 July 2007 (UTC)

I don't see the revelance of the two references. No 1 (the 1936 Erdős-Turán paper) does not, repeat does not mention this statement. I can only get the first page of the No. 2 reference which specifically mentions only Erdős' name ("these results have led Erdős to conjectue...") in connection witHe h this conjecture. So, why don't we agree that it is a conjecture of Erdős? Kope 14:25, 16 July 2007 (UTC)

For what it's worth, Green and Tao in their famous proof of the special case of the primes credit this to both Erdős and Turán.
CRGreathouse (t | c) 14:43, 16 July 2007 (UTC)

Well and they refer to the 1936 Erdos-Turan paper.... Let me quote one more paper of Erdos: Problems in number theory and combinatorics, Prooc. Sixth Manitoba Conf. on Num. Math., Congress Numer XVIII, 35-58. "Here I state the following old conjecture of mine: let a_1<a_2<\cdots be an infinite sequence of integers satisfying \sum \frac{1}{a_i}=\infty....". Kope 15:16, 16 July 2007 (UTC)

Yes, it was an old conjecture of his -- but it may have been one of Turan's as well, and that doesn't convince me otherwise. Richard Guy attributes it to both, and he's essentially the authority about these things. (I couldn't find anything in my biography, sadly -- maybe you have a batter one of Erdos? Or even better, one of Turan?)
CRGreathouse (t | c) 02:48, 17 July 2007 (UTC)

Thank you for the Green-Tao reference. I sent an email to Tao yesterday. He was easier to convince than you, as he already changed their Scholarpedia article on Szemerédi's theorem. Where does Guy attribute the conjecture to Turán? Kope 04:27, 17 July 2007 (UTC)

Excellent, that's someone who really is in the field. I haven't had luck in the past getting responses from Guy; he's a very busy man. You're welcome to email him if you think you'll have better luck. CRGreathouse (t | c) 12:33, 18 July 2007 (UTC)