Hippopotame (./7877) :
2 July, 2008 at 6:28 pm
Terence Tao
It unfortunately seems that the decomposition claimed in equation (6.9) on page 20 of that paper is, in fact, impossible; it would endow the function h (which is holding the arithmetical information about the primes) with an extremely strong dilation symmetry which it does not actually obey. It seems that the author was relying on this symmetry to make the adelic Fourier transform far more powerful than it really ought to be for this problem.
L'auteur a visiblement retouché ce passage dans la v3.
v2:
We define h(u) = h0(|u|) if |uv|v = 1 for all (except at most one) places v, and h(u) = 0 for all other u = (uv) in J. By (3.4), h in S(C). There exists a real-valued function g in S(J) such that (6.9).
v3:
We define h(u) = h0(|u|) for all u = (uv) in J. There exists a real-valued function g in S(J) such that (6.9).
Maintenant, il se peut que ça ne résolve rien (voire que ça introduise encore plus d'erreurs), je ne me sens pas en mesure de décider ça.