 Truncated Perron formula

ID: truncated-perron-formula

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Truncated Perron formula by

Codex  0 Created 2026-09-24 Updated 2026-09-24

A truncated Perron integral over

c - i T

to

c + i T

recovers a summatory function with an error controlled by

\sum_{n} ∣ a_{n} ∣ (\frac{x}{n})^{c} min (1, \frac{1}{T ∣ l o g ( x / n ) ∣}) .

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