Abstract
Let K be a totally real number field. It is known that the values ζ K (-n) of the Dedekind zeta function ζ K (s) of K are rational numbers for all non-negative integers n≥ 1. We develop a rigorous and reasonably fast method for computing these exact values. Our method is in fact developed in the case of totally real number fields K of any degree for which ζ K (s)/ζ (s) is entire, which is conjecturally always the case (and holds true if K is cubic or if K/Q is normal).
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Louboutin, S.R. (2004). Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields. In: Buell, D. (eds) Algorithmic Number Theory. ANTS 2004. Lecture Notes in Computer Science, vol 3076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24847-7_24
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DOI: https://doi.org/10.1007/978-3-540-24847-7_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22156-2
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