Structure and randomness in the prime numbers « What's new - 0 views
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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.
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3 July, 2008 at 3:41 am Gergely Harcos I also have some (perhaps milder) troubles with the proof. it seems to me as if Li had treated the Dirac delta on L^2(A) as a function. For example, the first 5 lines of page 28 make little sense to me. Am I missing something here?
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4 July, 2008 at 5:15 am Lior Silberman The function defined on page 20 does have a strong dilation symmetry: it is invariant by multiplication by ideles of norm one (since it is merely a function of the norm of ). In particular, it is invariant under multiplication by elements of . I’m probably missing something here. Probably the subtlety is in passing from integration over the nice space of idele classes to the singular space . The topologies on the spaces of adeles and ideles are quite different. There is a formal error in Theorem 3.1 which doesn’t affect the paper: the distribution discussed is not unique. A distribution supported at a point is a sum of derivatives of the delta distribution. Clearly there exist many such with a given special value of the Fourier transform. There is also something odd about this paper: nowhere is it pointed out what is the new contribution of the paper. Specifically, what is the new insight about number theory?
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