## Bombieri's Theorem

Define

 (1)

where
 (2)

(Davenport 1980, p. 121), is the Mangoldt Function, and is the Totient Function. Now define
 (3)

where the sum is over Relatively Prime to , , and
 (4)

Bombieri's theorem then says that for fixed,
 (5)

provided that .

References

Bombieri, E. On the Large Sieve.'' Mathematika 12, 201-225, 1965.

Davenport, H. Bombieri's Theorem.'' Ch. 28 in Multiplicative Number Theory, 2nd ed. New York: Springer-Verlag, pp. 161-168, 1980.