 Absolute convergence of cusp-form L-series from square coefficients

ID: absolute-convergence-of-cusp-form-l-series-from-square-coefficients

\sum ∣ a_{n} ∣^{2} n^{- β} < \infty

for

β > k

. Choose

k < β < 2 σ - 1

(\sum_{n \geq 1} ∣ a_{n} ∣^{2} n^{- β})^{1/2} (\sum_{n \geq 1} n^{- (2 σ - β)})^{1/2} < \infty.

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