Landau--Siegel zeros over varying number fields
Source: hexagonmath.org/abs/2611.00080v1
Let $K$ be a number field of degree $n$ and absolute discriminant $D_K$. We give a direct arithmetic proof that every real zero $\beta\in(0,1)$ of $\zeta_K$ satisfies \[ (1-\beta)\{\log D_K+n\log(2n)+6n+1\}\geq\frac1{1370}. \] The bound is explicit for arbitrary varying fields, including nonnormal fields, and gives $(1-\beta)\log D_K\gg1/\log(2n)$ for $K\ne\Q$. The proof combines OpenAI's determinant method, Masser's zero estimate as used by Kerr, and Banks' selected-embedding calculation. The resulting bound is expressed directly in the degree and discriminant of $K$, without introducing…
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