2025/05/22 by Saradha, N., Sharma, Divyum
#11D61 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2505.16465
Let F(x,y) be an irreducible form of degree r≥ 3 and having s+1 non-zero coefficients. Let h≥ 1 be an integer and consider the Thue inequality |F(x,y)|≤ h. Following the seminal work of Thue in 1909, several papers were written giving an upper bound for the number of solutions of the above inequality as ≪ c(r,s,h) where c(r,s,h) is an explicit function of r,s and h. Invariably, the absolute constant involved in ≪ has been left undetermined. In this paper, following Bombieri, Schmidt and Mueller, we give three different upper bounds which are explicit in every aspect.