Mathematics – Number Theory
Scientific paper
2003-05-29
Adv. Appl. Math. 36, no. 1 (2006), 1-29.
Mathematics
Number Theory
24 pages, 8 figures
Scientific paper
Higher-dimensional Dedekind sums are defined as a generalization of a recent 1-dimensional probability model of Dilcher and Girstmair to a d-dimensional cube. The analysis of the frequency distribution of marked lattice points leads to new formulae in certain special cases, and to new bounds for the classical Dedekind sums. Upper bounds for the generalized Dedekind sums are defined in terms of 1-dimensional moments. In the classical two-dimensional case, the ratio of these sums to their upper bounds are cosines of angles between certain vectors of n-dimensional cones, conjectured to have a largest spacial angle of pi/6.
Beck Matthias
Robins Sinai
Zacks Shelemyahu
No associations
LandOfFree
Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-607398