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

Bob Hough

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

Number Theory 2014-12-01 v2

Authors: Bob Hough

Abstract

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 $SL_2(\mathbb{Z})$ , 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.

Keywords

l-functions additive number theory modular forms

Cite

@article{arxiv.1109.1771,
  title  = {Zero density estimate for modular form $L$-functions in weight aspect},
  author = {Bob Hough},
  journal= {arXiv preprint arXiv:1109.1771},
  year   = {2014}
}

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