Algebroid function

Solution of equation with analytic coefficients

In mathematics, an algebroid function is a solution of an algebraic equation whose coefficients are analytic functions. So y(z) is an algebroid function if it satisfies

a d ( z ) y d + … + a 0 ( z ) = 0 , {\displaystyle a_{d}(z)y^{d}+\ldots +a_{0}(z)=0,}

where a k ( z ) {\displaystyle a_{k}(z)} are analytic.[1] If this equation is irreducible then the function is d-valued, and can be defined on a Riemann surface having d sheets.[2]


References

  1. ^ Yosida, Kosaku (1934), "On algebroid-solutions of ordinary differential equations", Jpn. J. Math., 10: 199–208
  2. ^ Hu, Pei Chu; Yang, Chung-Chun (1995), "The second main theorem for algebroid functions of several complex variables", Mathematische Zeitschrift, 220 (1): 99–126, doi:10.1007/BF02572605, MR 1347160


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