= Uniqueness of a possible exceptional real Dirichlet zero
{title2=$\#\{\beta\in[1-c/\log q,1]:L(\beta,\chi)=0\}\le1$}
For primitive real <nonprincipal Dirichlet characters>, there is an absolute $c>0$ with at most one zero in this interval, counted with multiplicity. Positivity of $-\zeta'/\zeta-L'/L$ and the local partial fractions give $0\le1/(\sigma-1)+C\log q-\sum(\sigma-\beta)^{-1}$. Testing $\sigma=1+a/\log q$ with small fixed $a$ rules out two nearby real zeros. Any possible zero is consequently simple; existence is not asserted.
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