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Coefficient bounds for level 2 cusp forms

Paul Jenkins; Kyle Pratt — 2015

Acta Arithmetica

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

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