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Central values of derivatives of Dirichlet L-functions

H. M. Bui and M. B. Milinovich
Arxiv ID: 0910.2051Last updated: 9/23/2021
Let C(q,+) be the set of even, primitive Dirichlet characters (mod q). Using the mollifier method we show that L^{(k)}(1/2,chi) is not equal to zero for almost all the characters chi in C(q,+) when k and q are large. Here, L^{(k)}(s,chi) is the k-th derivative of of the Dirichlet L-function L(s,chi).

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