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In mathematics, Vaughan's identity is an identity found by Template:Harvs that can be used to simplify Vinogradov's work on trigonometric sums. It can be used to estimate sums of the form

$\sum f(n)\Lambda (n)$

where f is some function of positive integers n, whose values in applications are often roots of unity, and Λ is the von Mangoldt function.

Vaughan's identity has been used to simplify the proof of the Bombieri–Vinogradov theorem and to study Kummer sums.

Vaughan's identity was generalized by Template:Harvtxt.

References

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