Euclidean rings of $S$-integers in complex quadratic fields
We give an elementary approach to studying whether rings of $S$-integers in complex quadratic fields are Euclidean with respect to the $S$-norm.
math.NT↗
arXiv subjects
Kyle Hammer
Publications and source records attributed to Kyle Hammer.
Skateboard Tricks and Topological Flips
We study the motion of skateboard flip tricks by modeling them as continuous curves in the group $SO(3)$ of special orthogonal matrices. We show that up to continuous deformation there are only four flip tricks. The proof relies on an analysis of the lift of such curves to the unit 3-sphere. We also derive explicit formulas for a number of tricks and continuous deformations between them.
math-ph↗
The special value $u=1$ of Artin-Ihara $L$-functions
We study the special value $u=1$ of Artin-Ihara $L$-functions associated to characters of the automorphism group of abelian covers of multigraphs. In particular, we show an annihilation statement analogous to a classical conjecture of Brumer on annihilation of class groups for abelian extensions of number fields and we also calculate the index of an ideal analogous to the classical Stickelberger ideal in algebraic number theory. Along the way, we make some observations about the number of spanning trees in abelian multigraph coverings that may be of independent interest.
math.NT↗