Elliott–Halberstam conjecture

In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter D. T. A. Elliott and Heini Halberstam, who stated the conjecture in 1968. where is Euler's totient function. If we then define the error function where the max is taken over all coprime to , then the Elliott–Halberstam conjecture is the assertion thatfor every and there exists a constant such that for all .

Elliott–Halberstam conjecture

In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter D. T. A. Elliott and Heini Halberstam, who stated the conjecture in 1968. where is Euler's totient function. If we then define the error function where the max is taken over all coprime to , then the Elliott–Halberstam conjecture is the assertion thatfor every and there exists a constant such that for all .