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Subconvexity bound for ${\rm GL}(2)$ $L$-functions: $t$-aspect

Volume 194 / 2020

Ratnadeep Acharya, Sumit Kumar, Gopal Maiti, Saurabh Kumar Singh Acta Arithmetica 194 (2020), 111-133 MSC: Primary 11F66, 11M41; Secondary 11F55. DOI: 10.4064/aa180711-9-5 Published online: 2 March 2020

Abstract

Let $F$ be a holomorphic Hecke eigenform or a Hecke–Maass cusp form for the full modular group ${\rm SL}(2, \mathbb {Z})$. We use the circle method to prove the Weyl exponent for ${\rm GL}(2)$ $L$-functions. We show that \[ L ( {1}/{2} + it, F ) \ll _{F, \epsilon } ( 2 + |t| )^{1/3 + \epsilon } \] for any $\epsilon \gt 0.$

Authors

  • Ratnadeep AcharyaHarish-Chandra Research Institute
    Chhatnag Road, Jhunsi
    Prayagraj (Allahabad) 211 019, India
    e-mail
  • Sumit KumarStat-Math Unit
    Indian Statistical Institute
    203 BT Road
    Kolkata 700108, India
    e-mail
  • Gopal MaitiStat-Math Unit
    Indian Statistical Institute
    203 BT Road
    Kolkata 700108, India
    e-mail
  • Saurabh Kumar SinghStat-Math Unit
    Indian Statistical Institute
    203 BT Road
    Kolkata 700108, India
    e-mail

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