 Fourier coefficient bound for a cusp form

ID: fourier-coefficient-bound-for-a-cusp-form

f (τ) = \sum_{n \geq 1} a_{n} q^{n}

k

level-one cusp form, boundedness of its invariant norm gives

∣ a_{n} ∣ = O (n^{k /2}) .

Integrate

f (x + i y) e^{- 2 πin x}

over one period and choose

y = 1/ n

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