Higher dimensional Dedekind sums in function fields

2012 ◽  
Vol 152 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Abdelmejid Bayad ◽  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Dedekind Sums ◽  
Higher Dimensional

Multiple Dedekind–Rademacher sums in function fields

2014 ◽  
Vol 10 (05) ◽  
pp. 1291-1307 ◽  
Author(s):  
Abdelmejid Bayad ◽  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Dedekind Sums ◽  
Reciprocity Law ◽  
Higher Dimensional

In the previous paper, we introduced the higher-dimensional Dedekind sums in function fields, and established the reciprocity law. In this paper, we generalize our higher-dimensional Dedekind sums and establish the reciprocity law and the Petersson–Knopp identity.

Dedekind sums and the transformation formula in function fields

2016 ◽  
Vol 12 (08) ◽  
pp. 2061-2072 ◽  
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Transformation Formula ◽  
Dedekind Sums ◽  
Dedekind Sum ◽  
Sum Formula

Dedekind used the classical Dedekind sum [Formula: see text] to describe the transformation of [Formula: see text] under the substitution [Formula: see text]. In this paper, we use the Dedekind sum [Formula: see text] in function fields to describe the transformation of a certain series under the substitution [Formula: see text].

Fractional parts of Dedekind sums in function fields

2015 ◽  
Vol 180 (3) ◽  
pp. 549-562
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Dedekind Sums

scholarly journals The ABC theorem for higher-dimensional function fields

2003 ◽  
Vol 356 (7) ◽  
pp. 2871-2887 ◽  
Author(s):  
Liang-Chung Hsia ◽  
Julie Tzu-Yueh Wang
Keyword(s):  
Function Fields ◽  
Higher Dimensional

Higher dimensional dedekind sums

1973 ◽  
Vol 202 (2) ◽  
pp. 149-172 ◽  
Author(s):  
Don Zagier
Keyword(s):  
Dedekind Sums ◽  
Higher Dimensional

Reconstruction of Higher-Dimensional Function Fields

2011 ◽  
Vol 11 (2) ◽  
pp. 185-204 ◽  
Author(s):  
F. Bogomolov ◽  
Yu. Tschinkel
Keyword(s):  
Function Fields ◽  
Higher Dimensional

scholarly journals Witten Volume Formulas for Semi-Simple Lie Algebras

Integers ◽  
2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Jianqiang Zhao
Keyword(s):  
Lie Algebras ◽  
Dedekind Sums ◽  
Combinatorial Method ◽  
Simple Lie Algebras ◽  
Higher Dimensional

AbstractIn this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in the computation of higher-dimensional Dedekind sums.

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