11F20 — 2 articles found.

Rationality of Dedekind Sums in Finite Fields

C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (4) 2012, pp. 105–111
Vol.34 (4) 2012
Yoshinori Hamahata Details
(Received: 2012-04-09 )
(Received: 2012-04-09 )

Yoshinori Hamahata, Institute for Teaching and Learning, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan; e-mail: hamahata@fc.ritsumei.ac.jp

Abstract/Résumé:

In Higher dimensional Dedekind sums in finite fields. Finite Fields Appl. 18 (2012), 19–25, we introduced the Dedekind–Zagier sum in finite fields. It is defined by a lattice $\Lambda$. The objective of this paper is to present a criterion for the rationality of our Dedekind–Zagier sum. For this purpose, we establish a connection between the field of definition of the exponential function for $\Lambda$ and the field of definition of the Dedekind–Zagier sum for $\Lambda$.

Dans Higher dimensional Dedekind sums in finite fields. Finite Fields Appl. 18 (2012), 19–25, nous avons introduit la somme de Dedekind–Zagier dans des corps finis. La somme est définie à partir d’un réseau $\Lambda$. L’objectif de ce travail est de présenter un critère de la rationalité de notre somme de Dedekind–Zagier. Pour le but, nous éstablissons la connexion entre le corps de définition de la fonction exponentielle pour $\Lambda$ et le corps de définition de notre somme de Dedekind–Zagier pour $\Lambda$.

Keywords: Dedekind sums, finite fields, lattices

AMS Subject Classification: Dedekind eta function; Dedekind sums 11F20

PDF(click to download): Rationality of Dedekind Sums in Finite Fields

Polynomials à la Lehmers and Wilf

C. R. Math. Rep. Acad. Sci. Canada Vol. 31 (3) 2009, pp. 65–71
Vol.31 (3) 2009
Gert Almkvist; Arne Meurman Details
(Received: 2009-01-23 )
(Received: 2009-01-23 )

Gert Almkvist, Centre for Mathematical Sciences, Mathematics, Lund University, Box 118, SE-221 00 Lund, Sweden; gert@maths.lth.se

Arne Meurman, Centre for Mathematical Sciences, Mathematics, Lund University, Box 118, SE-221 00 Lund, Sweden; arnem@maths.lth.se

Abstract/Résumé:

We show that a period polynomial introduced by the Lehmers coincides with a generalized Wilf polynomial.

Nous montrons qu’un polynôme période introduit par les Lehmer coïncide avec un polynôme de Wilf généralisé.

Keywords: period polynomial; Wilf polynomial; Dedekind sum

AMS Subject Classification: Dedekind eta function; Dedekind sums 11F20

PDF(click to download): Polynomials à la Lehmers and Wilf

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