Central values of derivatives of Dirichlet L-functions

Details Central values of derivatives of Dirichlet L-functions Central values of derivatives of Dirichlet L-functions

2009-10-11

arxiv.org/abs/0910.2051v3

Mathematics

Number Theory

submitted for publication

Scientific paper

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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