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| On the Upper Bound of the Number of Primes in Arithmetic Progression |
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Citation： |
Yao Qi.On the Upper Bound of the Number of Primes in Arithmetic Progression[J].Chinese Annals of Mathematics B,1987,8(4):449~453 |
| Page view： 792
Net amount： 647 |
Authors： |
Yao Qi; |
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| Abstract： |
Let a and q be relatively prime positive integers and \pi(x,q,a) stand for the number of primes p\leq x congruent to a and q. H. Iwanice proved that
\pi(x;q,q)<\frac{(2+\varepsilon)x}{\phi(q)log D}
for any \varepsilon>0, x>x_0 (\varepsilon) and q\leq x^9/20-\varepsilon , where D=xq^-3/8.
The author applies an improved estimation of the error term in the linear sieve, proves that for any \varepsilon>0, x>x_0 (\varepsilon) and q\leq x^5/11-\varepsilon , (1) is true. |
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