Algebroid function

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}+\ldots +a_{0}(z)=0,

where $a_{k}(z)$ 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

^ Yosida, Kosaku (1934), "On algebroid-solutions of ordinary differential equations", Jpn. J. Math., 10: 199–208, doi:10.4099/jjm1924.10.0_199
^ 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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[1] Yosida, Kosaku (1934), "On algebroid-solutions of ordinary differential equations", Jpn. J. Math., 10: 199–208, doi:10.4099/jjm1924.10.0_199

[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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