The Weyl bound for Dirichlet $L$-functions of cube-free conductor

Ian Petrow; Matthew P. Young

doi:https://doi.org/10.4007/annals.2020.192.2.3

Abstract

We prove a Weyl-exponent subconvex bound for any Dirichlet $L$-function of cube-free conductor. We also show a bound of the same strength for certain $L$-functions of self-dual $\mathrm {GL}_2$ automorphic forms that arise as twists of forms of smaller conductor.

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@ARTICLE{Milicevic, author = {Milićević, Djordje}, title = {Sub-{W}eyl subconvexity for {D}irichlet {$L$}-functions to prime power moduli}, journal = {Compos. Math.}, fjournal = {Compositio Mathematica}, volume = {152}, year = {2016}, number = {4}, pages = {825--875}, issn = {0010-437X}, mrclass = {11L07 (11L03 11L26 11L40 11M06 11S80 26E30)}, mrnumber = {3484115}, mrreviewer = {Arnaud Chadozeau}, doi = {10.1112/S0010437X15007381}, url = {https://doi.org/10.1112/S0010437X15007381}, zblnumber = {}, }
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@ARTICLE{PetrowYoung, author = {Petrow, Ian and Young, Matthew P.}, title = {A generalized cubic moment and the {P}etersson formula for newforms}, journal = {Math. Ann.}, fjournal = {Mathematische Annalen}, volume = {373}, year = {2019}, number = {1-2}, pages = {287--353}, issn = {0025-5831}, mrclass = {11F11 (11F37 11F66 11M06)}, mrnumber = {3968874}, mrreviewer = {Thomas Oliver}, doi = {10.1007/s00208-018-1745-1}, url = {https://doi.org/10.1007/s00208-018-1745-1}, zblnumber = {07051745}, }
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@ARTICLE{WuGL1timesGL2, author = {Wu, Han}, title = {Burgess-like subconvex bounds for {$\text{GL}_2\times\text{GL}_1$}}, journal = {Geom. Funct. Anal.}, fjournal = {Geometric and Functional Analysis}, volume = {24}, year = {2014}, number = {3}, pages = {968--1036}, issn = {1016-443X}, mrclass = {11F67 (11F70 22E55)}, mrnumber = {3213837}, mrreviewer = {Jannis A. Antoniadis}, doi = {10.1007/s00039-014-0277-4}, url = {https://doi.org/10.1007/s00039-014-0277-4}, zblnumber = {1376.11037}, }
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@ARTICLE{WuGL1, author = {Wu, Han}, title = {Burgess-like subconvexity for {${\rm GL}_1$}}, journal = {Compos. Math.}, fjournal = {Compositio Mathematica}, volume = {155}, year = {2019}, number = {8}, pages = {1457--1499}, issn = {0010-437X}, mrclass = {11F66 (11M06 11M41 11R42)}, mrnumber = {3977317}, mrreviewer = {Timothy Lee Gillespie}, doi = {10.1112/s0010437x19007309}, url = {https://doi.org/10.1112/s0010437x19007309}, zblnumber = {07077744}, }
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@ARTICLE{YoungCubic, author = {Young, Matthew P.}, title = {Weyl-type hybrid subconvexity bounds for twisted {$L$}-functions and {H}eegner points on shrinking sets}, journal = {J. Eur. Math. Soc. (JEMS)}, fjournal = {Journal of the European Mathematical Society (JEMS)}, volume = {19}, year = {2017}, number = {5}, pages = {1545--1576}, issn = {1435-9855}, mrclass = {11M41 (11F67 11M06)}, mrnumber = {3635360}, mrreviewer = {D. R. Heath-Brown}, doi = {10.4171/JEMS/699}, url = {https://doi.org/10.4171/JEMS/699}, zblnumber = {1430.11067}, }
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@ARTICLE{YoungEisenstein, author = {Young, Matthew P.}, title = {Explicit calculations with {E}isenstein series}, journal = {J. Number Theory}, fjournal = {Journal of Number Theory}, volume = {199}, year = {2019}, pages = {1--48}, issn = {0022-314X}, mrclass = {11F30 (11M36)}, mrnumber = {3926186}, mrreviewer = {Benjamin Linowitz}, doi = {10.1016/j.jnt.2018.11.007}, url = {https://doi.org/10.1016/j.jnt.2018.11.007}, zblnumber = {07030973}, }

The Weyl bound for Dirichlet $L$-functions of cube-free conductor

Abstract

Authors