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

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

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].

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.

scholarly journals Analogies of Dedekind sums in function fields

2010 ◽  
Vol 130 (8) ◽  
pp. 1750-1762 ◽  
Author(s):  
Shozo Okada
Keyword(s):  
Function Fields ◽  
Dedekind Sums

DENOMINATORS OF DEDEKIND SUMS IN FUNCTION FIELDS

2013 ◽  
Vol 09 (06) ◽  
pp. 1423-1430 ◽  
Author(s):  
YOSHINORI HAMAHATA
Keyword(s):  
Rational Function ◽  
Upper Bound ◽  
Function Fields ◽  
Dedekind Sums ◽  
Dedekind Sum

We consider the Dedekind sum s(a, c) in rational function fields. It is very similar to the classical Dedekind sum D(a, c). The objective of this study is to give a good upper bound of the degree of the denominator of s(a, c). As an application of our result, we present a condition on the elements a1, a2, and c of 𝔽q[T] such that s(a1, c) = s(a2, c).

Rationality of Dedekind sums in function fields

2012 ◽  
Vol 30 (3) ◽  
pp. 437-441
Author(s):  
Yoshinori Hamahata
Keyword(s):  
Function Fields ◽  
Dedekind Sums
Sign in / Sign up

Export Citation Format

Share Document