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math.NT2026
Integral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and Density
Angelot Behajaina, Pierre Dèbes, Martin Widmer
The Hilbert specialization property of a field, whereby irreducibility of polynomials is preserved under specialization of some of the variables, admits an integral counterpart whe…
math.NT2026
Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields
Christopher Frei, Efthymios Sofos, Martin Widmer
We prove an effective version of the Chebotarev density theorem, conditional on the quasi-Riemann hypothesis for the Dedekind zeta function. Drawing on recent breakthroughs of Open…