algebroid function

{{Short description|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

: $a_d(z)y^d + \ldots + a_0(z) = 0,$

where $a_k(z)$ are analytic.{{citation

| last = Yosida | first = Kosaku

| journal = Jpn. J. Math.

| pages = 199–208

| title = On algebroid-solutions of ordinary differential equations

| url = https://www.jstage.jst.go.jp/article/jjm1924/10/0/10_0_199/_pdf

| volume = 10

| year = 1934| doi = 10.4099/jjm1924.10.0_199

}} If this equation is irreducible then the function is d-valued,

and can be defined on a Riemann surface having d sheets.{{citation

| last1 = Hu | first1 = Pei Chu

| last2 = Yang | first2 = Chung-Chun

| doi = 10.1007/BF02572605

| issue = 1

| journal = Mathematische Zeitschrift

| mr = 1347160

| pages = 99–126

| title = The second main theorem for algebroid functions of several complex variables

| volume = 220

| year = 1995}}

References