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Coefficient bounds for level 2 cusp forms

Volume 168 / 2015

Paul Jenkins, Kyle Pratt Acta Arithmetica 168 (2015), 341-367 MSC: Primary 11F30. DOI: 10.4064/aa168-4-2


We give explicit upper bounds for the coefficients of arbitrary weight $k$, level 2 cusp forms, making Deligne's well-known $O(n^{(k-1)/{2}+\epsilon })$ bound precise. We also derive asymptotic formulas and explicit upper bounds for the coefficients of certain level 2 modular functions.


  • Paul JenkinsDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, U.S.A.
  • Kyle PrattDepartment of Mathematics
    The University of Illinois at Urbana-Champaign
    Urbana, IL 61801, U.S.A.

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