Doron Zeilberger's Email Message to Yuri Tschinkel (Feb. 14, 2012)

Dear Yuri,

As you already know, I am not interested in the Sills-Zeilberger Experimental Mathematics masterpiece to be reconsidered in ExpMath [as Jon Borwein kindly suggested] (or for that matter, any future paper of mine), but I am really interested in understanding the reasons behind the rejection. They are at least as interesting as the mathematical results in our paper!

On Feb. 23, 2012, (5:00-5:48pm) I am giving a talk at the Rutgers Experimental Mathematics Seminar BOTH explaining the content of the Sills-Z article, and trying to understand the attitudes, and reasonings, of the editors and referees of the three journals that rejected it.

It would really help me, if you could help clarify the puzzling (to me) comments made in the "referee" "report" (appended below), and especially the cryptic critique of Conj. 2.1. Based on the current evidence (and that's all we have, so far) our conjecture (2.1. in our paper) is VERY explicit, stating the oscillatory exponential growth of the Rademacher sequences and clearly stating the "period" (32), and the locations of the local maxima and minima. Also, this can certainly be a basis for future research, since it provides an ansatz for the asymptotic growth

C_{0,1,k}(32*m+i) \asympt C_{i,k}*mu_{i,k}^m*(Pol. in m corrections)

for some, yet-to-be-determined (most possibly by computers!) constants mu_{i,k} and C_{i,k} . This may lead to a computer-assisted rigorous proof of our clearly-stated conjecture.

Also the advise to read Rademacher is an empty one, there is nothing, only a few pages in his classic masterpiece. If your advice would have made sense, the great disciple of Rademacher, George Andrews, would have found a way.

Rademacher's intuition (false, as it turned out), that came from his seminal extension of the Hardy-Ramanujan asymptotic formula for the partition sequence, p(n), was due to confusing "far away" (to him, without computer evidence) with infinity, and we beautifully explain that in the last section (section 4) of our paper

Best wishes

Doron

P.S. Please respond. If you would ignore this message, I would also mention this fact in my talk and in the subsequent write-up. I will also post this message in my website (as an appendix to the above-mentioned writeup), and state that it received no response. On the other hand, if you do respond, I'll be glad to post your response (if you would permit) on my website.