The Bombieri–Vinogradov theorem is a significant result in analytic number theory, particularly in the study of prime numbers. It provides a statistical estimate for the distribution of prime numbers in arithmetic progressions. More specifically, the theorem states that, under certain conditions, the primes are uniformly distributed among the residues of a given modulus.
Articles by others on the same topic
For every there is such that, for ,Here is the Chebyshev function in an arithmetic progression and is the Euler totient function. Partial summation gives the corresponding result for the prime-counting function and the offset logarithmic integral function. The theorem controls the total error over many moduli; it need not give the same bound for each individual modulus.