The average behavior of the coefficients of Dedekind zeta function over square numbers☆

Publication year: 2011
Source: Journal of Number Theory, Volume 131, Issue 10, October 2011, Pages 1924-1938

Guangshi, Lü , Zhishan, Yang

In this paper, we are interested in the average behavior of the coefficients of Dedekind zeta function over square numbers. In Galois fields of degree d which is odd, when l⩾1 is an integer, we have where m=((d+1)/2)ldl−1, Pm(t) is a polynomial in t of degree m−1, and ε>0 is an arbitrarily small constant. By using our method, we also rectify the main terms of the k-dimensional divisor problem in some Galois fields over square numbers established by Deza and Varukhina (2008) [DV].