TY - JOUR

T1 - Representation of Small Integers by Binary Forms

AU - Akhtari, Shabnam

N1 - Publisher Copyright:
© 2015 Published by Oxford University Press.

PY - 2015/3/5

Y1 - 2015/3/5

N2 - We establish some upper bounds for the number of integer solutions to the Thue inequality |F(x, y)| ≤ m, where F is a binary form of degree n ≥ 3 and with non-zero discriminant D, and m is an integer. Our upper bounds are independent of m, when m is smaller than |D|1/4(n-1). We also consider the Thue equation |F(x, y)| = m and give some upper bounds for the number of its integral solutions. In the case of equation, our upper bounds will be independent of integer m, when m |D|1/2(n-1).

AB - We establish some upper bounds for the number of integer solutions to the Thue inequality |F(x, y)| ≤ m, where F is a binary form of degree n ≥ 3 and with non-zero discriminant D, and m is an integer. Our upper bounds are independent of m, when m is smaller than |D|1/4(n-1). We also consider the Thue equation |F(x, y)| = m and give some upper bounds for the number of its integral solutions. In the case of equation, our upper bounds will be independent of integer m, when m |D|1/2(n-1).

UR - http://www.scopus.com/inward/record.url?scp=84952308954&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952308954&partnerID=8YFLogxK

U2 - 10.1093/qmath/hav026

DO - 10.1093/qmath/hav026

M3 - Article

AN - SCOPUS:84952308954

SN - 0033-5606

VL - 66

SP - 1009

EP - 1054

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 4

ER -