Computation of Stiefel filtering function via genus 2 theta functions

The problem of best uniform rational approximation of signum function on two segments of real line was solved by E.Zolotarev in 1877 in terms of elliptic functions. Ed Stiefel continued this research and solved the natural extention of this problem to three bands in 1961. We develop an approach to evaluate Stiefel solutions via computations with genus 2 Riemann theta functions. (Joint work with A.B.Bogatyrev and T.R.Garaev)