An improved zero-free half-plane for Hecke L-functions over number fields and Quasi-Riemann Hypothesis
In this paper, we obtain a zero-free half-plane Re(s) > B∗ for every finite-order Hecke L- function over every number field, where B∗ = 0.87446830769353045955... is an explicitly defined algebraic number. This improves the Quasi-Riemann Hypothesis over arbitrary num- ber fields. The proof refines the cubic-theta comparison. A sharper amplified Gauss-norm estimate permits a longer additional prime product, chosen separately for each dyadic sum- mation length. Combining the resulting moment saving with contour displacement on the same dyadic sum gives the principal improvement. The enlarged…
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