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

VL - 56

SP - 199

EP - 213

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

IS - 1-4

ER -