Multiple Dedekind–Rademacher sums in function fields

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.

Download Full-text

Higher dimensional Dedekind sums in function fields

Acta Arithmetica ◽

10.4064/aa152-1-6 ◽

2012 ◽

Vol 152 (1) ◽

pp. 71-80 ◽

Cited By ~ 11

Author(s):

Abdelmejid Bayad ◽

Yoshinori Hamahata

Keyword(s):

Function Fields ◽

Dedekind Sums ◽

Higher Dimensional

Download Full-text

Rademacher’s reciprocity law for Dedekind sums in function fields

Monatshefte für Mathematik ◽

10.1007/s00605-013-0559-1 ◽

2013 ◽

Vol 174 (3) ◽

pp. 449-458

Author(s):

Yoshinori Hamahata

Keyword(s):

Function Fields ◽

Dedekind Sums ◽

Reciprocity Law

Download Full-text

The triple reciprocity law for the twisted second moments of Dirichlet $L$-functions over function fields

Proceedings of the American Mathematical Society ◽

10.1090/proc/15507 ◽

2021 ◽

pp. 1

Author(s):

Goran Djanković ◽

Dragan Đokić ◽

Nikola Lelas

Keyword(s):

Function Fields ◽

Reciprocity Law ◽

Second Moments

Download Full-text

Brauer groups of curves and reciprocity law in Brauer groups of their function fields

Algebra ◽

10.1515/9783110805697.379 ◽

2012 ◽

Author(s):

V. I. Yanchevskii

Keyword(s):

Function Fields ◽

Brauer Groups ◽

Reciprocity Law

Download Full-text

Dedekind sums and the transformation formula in function fields

International Journal of Number Theory ◽

10.1142/s1793042116501232 ◽

2016 ◽

Vol 12 (08) ◽

pp. 2061-2072 ◽

Cited By ~ 1

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].

Download Full-text

Franel integrals of order four

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700037599 ◽

1996 ◽

Vol 60 (2) ◽

pp. 192-203 ◽

Cited By ~ 1

Author(s):

Richard J. McIntosh

Keyword(s):

Lattice Point ◽

Elementary Proof ◽

Unit Interval ◽

Dedekind Sums ◽

Dedekind Sum ◽

Elementary Method ◽

The Third ◽

Reciprocity Law ◽

Order Four

AbstractLet ((x)) =x−⌊x⌋−1/2 be the swatooth function. Ifa, b, cand e are positive integeral, then the integral or ((ax)) ((bx)) ((cx)) ((ex)) over the unit interval involves Apolstol's generalized Dedekind sums. By expressing this integral as a lattice-point sum we obtain an elementary method for its evaluation. We also give an elementary proof of the reciprocity law for the third generalized Dedekind sum.

Download Full-text