A VARIANT OF THE BARBAN-DAVENPORT-HALBERSTAM THEOREM

作者：Smith Ethan^*

来源：International Journal of Number Theory, 2011, 7(8): 2203-2218.

DOI：10.1142/S179304211100499X

• Barban-Davenport-Halberstam Theorem
• Chebotarev Density Theorem
• large sieve

Let L/K be a Galois extension of number fields. The problem of counting the number of prime ideals p of K with fixed Frobenius class in Gal(L/K) and norm satisfying a congruence condition is considered. We show that the square of the error term arising from the Chebotarev Density Theorem for this problem is small "on average". The result may be viewed as a variation on the classical Barban-Davenport-Halberstam Theorem.

• 出版日期2011-12