Non-vanishing of Dirichlet L-functions at the central point

Mathematics – Number Theory

Scientific paper

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19 pages

Scientific paper

Let $\chi$ be a primitive Dirichlet character modulo $q$ and $L(s,\chi)$ be
the Dirichlet L-function associated to $\chi$. Using a new two-piece mollifier
we show that $L(\tfrac{1}{2},\chi)\ne0$ for at least 34% of the characters in
the family.

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