Abstract
In the previous paper we introduced the higher dimensional Dedekind sum in a function field (Bayad and Hamahata, Acta Arith. 152:71–80, 2012). The purpose of this paper is to present a criterion for the rationality of our Dedekind sum. To do so, we establish a connection between the field of definition of the Drinfeld module ϕ and the field of definition of the higher dimensional Dedekind sum s Λ (a 0;a 1,…,a d ) associated to the A-lattice Λ, which corresponds to ϕ.
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The author expresses his sincere gratitude to the referee for reading the manuscript carefully and giving helpful advice.
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Hamahata, Y. Rationality of Dedekind sums in function fields. Ramanujan J 30, 437–441 (2013). https://doi.org/10.1007/s11139-012-9402-x
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DOI: https://doi.org/10.1007/s11139-012-9402-x