Coefficient Bounds for Level 2 Cusp Forms and Modular Functions

preprint2014arXivOpen access

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

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Coefficient Bounds for Level 2 Cusp Forms and Modular Functions

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