RBerenguel: First: Why? Second: What? (I arrived 20 minuts ago from taking a few beers.... can't think properly.) Third: Why you edit here? (I don't mean you can't, just what's the purpose of your question, now I can't see it... two beer or not two beer, you know?)
ilan: It is absolutely relevant to this page, you just have to figure out the answer to the question.
ilan: Yes, these operators were invented by Hecke to prove that that the L-function associated to a holomorphic modular form had an Euler product (the initially conjecture of Ramanujan for the Delta function was proved by Mordell). You can view Hecke operators as p-adic analogues of the Laplacian, since this can be viewed as the centre of the universal enveloping algebra of SL(2, R). Now maybe you can figure out what I wrote.
RBerenguel: Good answer!, seems you know more about them than I... but I have all summer to learn about it. But I still can't see what do you meant with your first question.
JohnKeats: Just guessing Ilan... but my teacher of Algebraic Geometry introduced us in a problem Catalan numbers (related with some Hilbert polynomials and certain degrees, can't remember exactly) and made us look it in a great book of such things... I think that your problem appears there, associated with that succession, which seems to be everywhere. May it be? (I won't solve that because such things always piss me off and I try not to do so). Anyway, the 5th Catalan Number is the answer to the Ultimate Question to Life, the Universe and Everything, if you know what I mean :D
ilan: That is correct, as well as the correct solution method: you could guess the answer from my assertion that the problem had everything to do with your page. On the other hand, I suggest that if you want to continue your math studies, that you start liking solving such problems: no matter how advanced your thesis problem will be, its solution will come down to something fairly similar to the solution of such a problem. Or think of it this way: it is like trying to become a professional in go without liking life and death problems. For future reference, this is how to solve problems like the one I gave you: (A) Compute the number for the first few cases N = 1,2,3,4,5. (B) Input these numbers into the Encyclopedia of Integer Sequences (C) Find a candidate sequence (D) Look up this sequence to see if the problem has already been solved (E) Solve it yourself if it hasn't.
JohnKeats: No thesis yet, I still have one year ahead. I don't mean I don't like such problems in a general way, but this one type of "counting" things... I'm a future mathematician who hates counting :D Anyway, thanks for posting that problem (very related, I'll move everything to discussion except the question) and too helping with the answer ;)
ilan: As you probably know, there are three types of mathematicians, the ones who like counting and the ones who don't.
JohnKeats: I'm one of the other third, I think ;)