Landen transforms as families of (commuting) rational self-maps of projective space

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Joyce, Michael; Kawaguchi, Shu; Silverman, Joseph H.;
  • Subject: Primary: 14E05, Secondary: 37P05 | Mathematics - Algebraic Geometry | Mathematics - Dynamical Systems | Mathematics - Number Theory

The classical (m,k)-Landen transform F_{m,k} is a self-map of the field of rational functions C(z) obtained by forming a weighted average of a rational function over twists by m'th roots of unity. Identifying the set of rational maps of degree d with an affine open subs... View more
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