Sur la quasi-convexité des arcs trinomiaux

@article{Dubuc1996SurLQ,
  title={Sur la quasi-convexit{\'e} des arcs trinomiaux},
  author={Serge Dubuc and Mohammed Zaoui},
  journal={Rendiconti del Circolo Matematico di Palermo},
  year={1996},
  volume={45},
  pages={493-514}
}
From the equationpn−k sinnθ−ρn sin(n−k)θ=sinkθ we will show that the function σ=σ(θ) is increasing for the arcsAm, obtained when one putsn=m, k=m−1 andm=3,4,5,… Next, we will study the arcsBm obtained whenn=m, k=m−2 andm an odd integer larger than 3. In this case, σ(θ) will be shown to be a decreasing function. Finally, the Farey arcsF(p,q;r,s) are obtained whenn=s, k=q, s andq relatively prime. It will be proved that the function σ(θ) is strictly quasi-convex. 

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