Electronic Resource
Springer
Monatshefte für Mathematik
106 (1988), S. 211-219
ISSN:
1436-5081
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetK be a cubic number field. Denote byA K (x) the number of ideals with ideal norm ≤x, and byQ K (x) the corresponding number of squarefree ideals. The following asymptotics are proved. For every ε〉0 ε〉0 $$\begin{gathered} {\text{ }}A_K (x) = c_1 x + O(x^{43/96 + \in } ), \hfill \\ Q_K (x) = c_2 x + O(x^{1/2} \exp {\text{ }}\{ - c(\log {\text{ }}x)^{3/5} (\log \log {\text{ }}x)^{ - 1/5} \} ). \hfill \\ \end{gathered}$$ Herec 1,c 2 andc are positive constants. Assuming the Riemann hypotheses for the Dedekind zeta function ζ K , the error term in the second result can be improved toO(x 53/116+ε).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01318682
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