Algebraic curves P(x)-Q(y)=0 and functional equations

F. Pakovich

doi:10.1080/17476930903394838

Algebraic curves P(x)-Q(y)=0 and functional equations

F. Pakovich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

In this article, we give several conditions implying the irreducibility of the algebraic curve P(x)-Q(y)=0, where P, Q are rational functions. We also apply the results obtained to the functional equations P(f)=Q(g) and P(f)=cP(g), where c εC For example, we show that for a generic pair of rational functions P, Q the first equation has no non-constant solutions f, g meromorphic on C whenever (degP-1)(degQ-1)≥2.

Original language	English
Pages (from-to)	199-213
Number of pages	15
Journal	Complex Variables and Elliptic Equations
Volume	56
Issue number	1-4
DOIs	https://doi.org/10.1080/17476930903394838
State	Published - 1 Jan 2011

Keywords

Algebraic curves
Compositions
Functional equations
Meromorphic functions
Monodromy groups
Strong uniqueness polynomials

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1080/17476930903394838

Cite this

@article{08cea2cea69140b1b74e1869b40073a8,

title = "Algebraic curves P(x)-Q(y)=0 and functional equations",

abstract = "In this article, we give several conditions implying the irreducibility of the algebraic curve P(x)-Q(y)=0, where P, Q are rational functions. We also apply the results obtained to the functional equations P(f)=Q(g) and P(f)=cP(g), where c εC For example, we show that for a generic pair of rational functions P, Q the first equation has no non-constant solutions f, g meromorphic on C whenever (degP-1)(degQ-1)≥2.",

keywords = "Algebraic curves, Compositions, Functional equations, Meromorphic functions, Monodromy groups, Strong uniqueness polynomials",

author = "F. Pakovich",

note = "Funding Information: The author was supported by ISF, Grant No. 979/05.",

year = "2011",

month = jan,

day = "1",

doi = "10.1080/17476930903394838",

language = "English",

volume = "56",

pages = "199--213",

journal = "Complex Variables and Elliptic Equations",

issn = "1747-6933",

publisher = "Taylor and Francis Ltd.",

number = "1-4",

}

TY - JOUR

T1 - Algebraic curves P(x)-Q(y)=0 and functional equations

AU - Pakovich, F.

N1 - Funding Information: The author was supported by ISF, Grant No. 979/05.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - In this article, we give several conditions implying the irreducibility of the algebraic curve P(x)-Q(y)=0, where P, Q are rational functions. We also apply the results obtained to the functional equations P(f)=Q(g) and P(f)=cP(g), where c εC For example, we show that for a generic pair of rational functions P, Q the first equation has no non-constant solutions f, g meromorphic on C whenever (degP-1)(degQ-1)≥2.

AB - In this article, we give several conditions implying the irreducibility of the algebraic curve P(x)-Q(y)=0, where P, Q are rational functions. We also apply the results obtained to the functional equations P(f)=Q(g) and P(f)=cP(g), where c εC For example, we show that for a generic pair of rational functions P, Q the first equation has no non-constant solutions f, g meromorphic on C whenever (degP-1)(degQ-1)≥2.

KW - Algebraic curves

KW - Compositions

KW - Functional equations

KW - Meromorphic functions

KW - Monodromy groups

KW - Strong uniqueness polynomials

UR - http://www.scopus.com/inward/record.url?scp=79951803086&partnerID=8YFLogxK

U2 - 10.1080/17476930903394838

DO - 10.1080/17476930903394838

M3 - Article

AN - SCOPUS:79951803086

SN - 1747-6933

VL - 56

SP - 199

EP - 213

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 1-4

ER -

Algebraic curves P(x)-Q(y)=0 and functional equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this