Explicit formulae for primes in arithmetic progressions, I

Original · EN

We shall give an explicit formula for ψ(x, q, a) with an error term of the form C/αx under the condition that q<α¹ x is nonexceptional, for various values of α and α₁. We shall also give an explicit formula for ψ(x, q, a) with error terms C/ᵃ x working whether q is exceptional or nonexceptional, but under the condition that 0.4923Aπq¹/²² q< x/ x. Moreover, we shall give an explicit form of Bombieri-Vinogradov theorem over non-exceptional moduli.