Selected character moments, zero-free half-planes for Hecke L-functions over number fields, and Quasi-Riemann Hypothesis
Source: hexagonmath.org/abs/2611.00082v1
In this paper, we obtain a zero-free half-plane $\Rea s>B_2$ for every finite-order Hecke $L$-function over every number field, where \[ B_2=\frac{777-\sqrt{1081}}{852} =0.873381966613207519929\ldots. \] We adapt selected character-sum estimates and finite moment inductions to ideal-character sums over arbitrary number fields and restore ordinary sixth powers. Two finite moment inductions give an ordinary product estimate with length condition $n_1+n_2+2z\le M$ for sufficiently fine original prime factors. Applying this estimate to zero detection and the averaged numerator in the cubic-theta…
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