Fixed points of matrices have many applications in various areas science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the 2×22×2 with integer entries determinant ±1±1. There are strong connections between extended group, continued fractions Farey graph. graph a vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider elements that fix rationals. For given rational number, use its neighbour...

Weyl group multiple Dirichlet series are in r complex variables, with analytic continuation to Cr and a of functional equations isomorphic the reduced root system rank r. Such may be defined for any global field K, but case when K is an algebraic function they expected be, up variable change, rational functions several variables. We verify rationality these K=Fq(T), describe denominators suppor...