Abstract
Let \(F(X,Y)=\sum \limits _{i=0}^sa_iX^{r_i}Y^{r-r_i}\in \mathbb {Z}[X,Y]\) be a form of degree \(r\ge 3\), irreducible over \(\mathbb {Q}\), and having at most \(s+1\) nonzero coefficients. Mueller and Schmidt showed that the number of solutions of the Thue inequality
is \(\ll s^2h^{2/r}(1+\log h^{1/r})\). They conjectured that \(s^2\) may be replaced by s. In this note we show some instances when \(s^2\) may be improved.
This paper is dedicated to Krishna Alladi on the occasion of his 60th birthday
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Saradha, N., Sharma, D. (2017). A Note on Thue Inequalities with Few Coefficients. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_36
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