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The classical zeta region is not a uniform dirichlet l region
Discussion
The classical region Riemann zeta classical zero free region is a statement about zeta with an absolute constant. The progression theorem Prime number theorem arithmetic progressions fixes q before its character transforms and contour neighborhoods are chosen. Its argument supplies neither a rate uniform as q grows nor a uniform Dirichlet L-function zero-free region. No existence of exceptional real zeros is claimed here; this is a scope distinction, not a counterexample to an asserted uniform theorem.
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Sources
- §6.1.1, paragraph following Exercise 4, p.176 (standard reference, not scraped)