Functiones et Approximatio Commentarii Mathematici
- Funct. Approx. Comment. Math.
- Volume 53, Number 1 (2015), 31-45.
On the ideal theorem for number fields
Let $K$ be an algebraic number field and $\nu_K$ be the ideal-counting function of $K$. Many authors have estimated the remainder term $\Delta_n(x,K)$ in the asymptotic formula of the average order of $\nu_K$. The purpose of this work is twofold: we first generalize Müller's method to the $n$-dimensional case and improve on Nowak's result. A key part in the proof is played by a~profound result on a triple exponential sum recently derived by Robert \& Sargos.
Funct. Approx. Comment. Math., Volume 53, Number 1 (2015), 31-45.
First available in Project Euclid: 28 September 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Bordellès, Oliver. On the ideal theorem for number fields. Funct. Approx. Comment. Math. 53 (2015), no. 1, 31--45. doi:10.7169/facm/2015.53.1.3. https://projecteuclid.org/euclid.facm/1443444849