Functiones et Approximatio Commentarii Mathematici

On the ideal theorem for number fields

Oliver Bordellès

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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.

Article information

Funct. Approx. Comment. Math., Volume 53, Number 1 (2015), 31-45.

First available in Project Euclid: 28 September 2015

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11N37: Asymptotic results on arithmetic functions
Secondary: 11L07: Estimates on exponential sums 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]

ideal theorem Voronoi-Atkinson type formula exponential sums of type I and II


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.

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