Zero density estimate for modular form $L$-functions in weight aspect

Details Zero density estimate for modular form $L$-functions in weight aspect Zero density estimate for modular form $L$-functions in weight aspect

2011-09-08

arxiv.org/abs/1109.1771v1

Mathematics

Number Theory

Scientific paper

Considering the family of $L$-functions $\{L(s,f)\}_{f \in H_k}$ where $H_k$
is the set of weight $k$ Hecke-eigen cusp forms for $SL_2(\zed)$, we prove a
zero density estimate near the central point, valid as the weight $k \to
\infty$. This is an ingredient in the author's related paper, which gives an
unconditional upper bound on the distribution of the central values.

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