An explicit radical parametrization of Zolotarev polynomials of degree 7 in terms of nested square rootsH.-J. Rack, R. VajdaThe problem of determining a family of normalized n-th degree Zolotarev polynomials Zn,t on [-1,1] in the form Zn,t(x)=ānk=0bk,n(t) xk has been solved for n ā¤ 6. Here bk,n(t), with bn,n(t) ā 0 and parameter t, are explicit closed-form expressions for the coefficients of Zn,t. Such parametrizations are rational for n<5 and simple radical for nā{5,6}. In this work we settle the case n=7 by providing a nonsimple, nested radical parametrization. We have used symbolic computation and parametrization of algebraic curves to derive the formulae for bk,7(t). The case n=7 requires special attention because the associated reduced relation curve is a non-hyperelliptic algebraic curve of genus 4, contrary to the quintic and sextic cases where the reduced relation curve is elliptic.Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 14(4) (2021), pp. 37-60 |