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Subconvexity for $L$-functions of non-spherical cusp forms on ${\rm GL}(3)$

Volume 192 / 2020

Valentin Blomer, Jack Buttcane Acta Arithmetica 192 (2020), 31-62 MSC: Primary 11M41, 11F55, 11F72. DOI: 10.4064/aa180125-5-2 Published online: 24 October 2019


Let $f$ be a cusp form for ${\rm SL}(3, \Bbb {Z})$ associated with a generalized principal series representation of minimal weight $d$, spectral parameter $r$ and associated $L$-function $L(s, f)$. For $r \asymp d \asymp T$ the subconvexity bound $L(1/2, f) \ll T^{3/4 - 1/140000 }$ is proved.


  • Valentin BlomerMathematisches Institut
    Universität Bonn
    Endenicher Allee 60
    D-53115 Bonn, Germany
  • Jack ButtcaneDepartment of Mathematics and Statistics
    University of Maine
    5752 Neville Hall, Room 333
    Orono, ME 04469, U.S.A.

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