Seminar Details

By constructing custom "chimera" functions from Dirichlet L-functions, we create self-dual test objects whose true zero distributions are independently verifiable through contour counts using the argument principle. When standard critical-line verification algorithms are run on these self-dual chimeras, we discover a remarkable phenomenon. The line instrument is exact on the critical line, but it remains entirely silent regarding zeros sitting beside it. An unbroken sequence of on-line findings is precisely what a line-restricted instrument returns, whether the adjacent strip is empty or not. In the second half of the talk, we will trace this structural failure of verification back to its logical origins, and re-examine five historical proofs of the Prime Number Theorem. We will see how classical proofs by contradiction in analytic number theory rely on an unexamined 1905 convention of logic, where a failure of the analytic language to form a valid term around an off-line zero is conflated with a logical refutation.