Explicit formulae for primes in arithmetic progressions, I

We shall give an explicit formula for $ψ(x, q, a)$ with an error term of the form $C/\log^αx$ under the condition that $q<\log^{α_1} x$ is nonexceptional, for various values of $α$ and $α_1$. We shall also give an explicit formula for $ψ(x, q, a)$ with error terms $C/\log^A x$ working whether $q$ is exceptional or nonexceptional, but under the condition that $\frac{0.4923A}πq^{1/2}\log^2 q<\log x/\log\log x$. Moreover, we shall give an explicit form of Bombieri-Vinogradov theorem over non-exceptional moduli.

No reviews yet.

No comments yet.