From eb@IAS.EDU Tue Apr 1 12:35:50 1997 Received: from IAS.EDU (mailgate.ias.edu [192.16.204.20]) by euclid.math.temple.edu (8.8.5/8.8.5) with SMTP id MAA22148 for ; Tue, 1 Apr 1997 12:35:49 -0500 (EST) Received: from sevilla.math.ias.edu (sevilla.math.ias.edu [192.108.106.26]) by IAS.EDU (8.6.12/8.6.12) with ESMTP id MAA01386 for ; Tue, 1 Apr 1997 12:35:14 -0500 Received: from portland.math.ias.edu (portland.math.ias.edu [192.108.106.23]) by sevilla.math.ias.edu (8.6.12/8.6.12) with ESMTP id MAA28295; Tue, 1 Apr 1997 12:35:15 -0500 From: Enrico Bombieri Received: (eb@localhost) by portland.math.ias.edu (8.6.12/8.6.12) id MAA20423; Tue, 1 Apr 1997 12:35:12 -0500 Date: Tue, 1 Apr 1997 12:35:12 -0500 Message-Id: <199704011735.MAA20423@portland.math.ias.edu> To: eb@IAS.EDU, zeilberg@euclid.math.temple.edu Content-Length: 1151 Status: RO Dear Doron, There are fantastic developments to Alain Connes's lecture at IAS last Wednesday. Connes gave an account of how to obtain a trace formula involving zeroes of L-functions only on the critical line, and the hope was that one could obtain also Weil's explicit formula in the same context; this would solve the Riemann hypothesis for all L-functions at one stroke. Thus there cannot be even a single zeroe(1) off the critical line! Well, a young physicist at the lecture saw in a flash that one could set the whole thing in a combinatorial setting using supersymmetric fermionic-bosonic systems (the physics corresponds to a near absolute zero ensemble of a mixture of anyons and morons with opposite spins) and, using the C-based meta-language MISPAR, after six days of uninterrupted work, computed the logdet of the resolvent Laplacian, removed the infinities using renormalization, and, lo and behold, he got the required positivity of Weil's explicit formula! Wow! Regards also from Paula Cohen. Please give this the highest diffusion. Best, Enrico (1) This is the correct spelling, according to vicepresident Dan Quayle.