An explicit elementary proof of no Landau--Siegel zeros
We give an elementary proof of the absence of Landau--Siegel zeros with the explicit constant $c=1/100$. For every primitive quadratic Dirichlet character $\chi$ of conductor $q\ge3$, each real zero $\beta\in(0,1)$ of $L(s,\chi)$ satisfies $(1-\beta)\log q>c$. The proof combines integer coefficient counting, polynomial congruences, a paired-tail hyperbola estimate, and a logarithmically weighted comparison of positive sums. All required constants are explicit, and one choice of parameters covers every conductor. The argument uses elementary arithmetic and real summation and integration,…
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