Explicit formulae for L-functions: Difference between revisions

Revision as of 21:32, 6 September 2007

Revision as of 21:33, 6 September 2007

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In terms suggested by the [[Hilbert-Pólya conjecture]], one of the major heuristics underlying the [[Riemann hypothesis]] and its supposed connection with [[functional analysis]], the complex zeroes ρ should be closely linked to the [[eigenvalue]]s of some [[linear operator]] ''T''. A sum

:<math> \Sigmasum = \Sigma_sum_{\rho} F(\rho) \,</math>

would then have this interpretation: use the [[functional calculus]] of operators, supposed to apply to ''T'', to form