t-Aspect Subconvexity Bound for $GL(2)$ L-functions

Keshav Aggarwal; Saurabh Kumar Singh

t-Aspect Subconvexity Bound for $GL(2)$ L-functions

Number Theory 2018-04-20 v2

Authors: Keshav Aggarwal , Saurabh Kumar Singh

Abstract

Let $f$ be a holomorphic Hecke eigenforms or a Hecke-Maass cusp form for the full modular group $SL(2, \mathbb{Z})$ . In this paper we shall use circle method to prove the Weyl exponent for $GL(2)$ $L$ -functions. We shall prove that $L \left( \frac{1}{2} + it \right) \ll_{f, \epsilon} \left( 1 + |t|\right)^{1/3 + \epsilon},$ for any $\epsilon > 0.$

Keywords

l-functions weyl groups and algebras modular forms

Cite

@article{arxiv.1706.04977,
  title  = {t-Aspect Subconvexity Bound for $GL(2)$ L-functions},
  author = {Keshav Aggarwal and Saurabh Kumar Singh},
  journal= {arXiv preprint arXiv:1706.04977},
  year   = {2018}
}

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Second version version

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