Timeline for Are these powers of a characteristic 3 power series annihilated by certain Hecke operators?
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| Oct 25, 2013 at 16:44 | comment | added | paul Monsky | Just to make the comment of mine that I'm replacing clearer: When p is 2 mod 3 and w is odd, p^(w-1)+1 is 2, not 0 in Z/3Z. So the end of Noam's proof is wrong. A revision is: ... ,whence c_(np)=c(n/p) where c_n is the coefficient of x^n in D^k. Now the coefficient of x^n in T_p(D^k) is c_(np)+p*c(n/p); since p is 2 mod 3, this is 0. (One thing to note is that in characteristics ell=2 or 3, when p isn't ell then for even w, p^(w-1)=p. So one can define formal Hecke operators on Z/ell[[x]] without taking the weight into effect, that will act well on reductions of forms of any even degree. | |
| Oct 22, 2013 at 6:52 | comment | added | paul Monsky | Thanks, Noam. The argument also occurred to me just after I submitted the question. I wonder if you have any ideas about my deeper question--is the space spanned by the D^j with j prime to 6 stable under the T_n with n prime to 6? It certainly seems true experimentally. | |
| Oct 22, 2013 at 5:38 | vote | accept | paul Monsky | ||
| Oct 22, 2013 at 3:47 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |