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).
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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 -