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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…
math.NT2026
Serre's problem on statistics of Brauer symbols
Efthymios Sofos
We solve Serre's problem on the specialisation of Brauer group elements in all cases where the number of variables is sufficiently large.
math.NT2026
Counting square-free values of random polynomials
Efthymios Sofos
We prove that the average error term when counting square-free values of polynomials is the quartic root of the main term.