Bombieri,s Theorem
المؤلف:
Bombieri, E.
المصدر:
"On the Large Sieve." Mathematika 12
الجزء والصفحة:
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16-8-2020
1446
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.
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