TY - JOUR
T1 - Thue’s inequalities and the hypergeometric method
AU - Akhtari, Shabnam
AU - Saradha, N.
AU - Sharma, Divyum
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media New York.
PY - 2018/2/1
Y1 - 2018/2/1
N2 - We establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0 < | F(x, y) | ≤ h, where F(x, y) = (αx+ βy) r- (γx+ δy) r∈ Z[x, y] , α, β, γ and δ are algebraic constants with αδ- 0 , and r≥ 5 and h are integers. As an important application, we pay special attention to binomial Thue’s inequalities | axr- byr| ≤ c. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement by Evertse.
AB - We establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0 < | F(x, y) | ≤ h, where F(x, y) = (αx+ βy) r- (γx+ δy) r∈ Z[x, y] , α, β, γ and δ are algebraic constants with αδ- 0 , and r≥ 5 and h are integers. As an important application, we pay special attention to binomial Thue’s inequalities | axr- byr| ≤ c. The proofs are based on the hypergeometric method of Thue and Siegel and its refinement by Evertse.
UR - https://www.scopus.com/pages/publications/85015634330
UR - https://www.scopus.com/pages/publications/85015634330#tab=citedBy
U2 - 10.1007/s11139-017-9887-4
DO - 10.1007/s11139-017-9887-4
M3 - Article
AN - SCOPUS:85015634330
SN - 1382-4090
VL - 45
SP - 521
EP - 567
JO - Ramanujan Journal
JF - Ramanujan Journal
IS - 2
ER -