Explicit and Mixed Estimates for Thue inequalities with few coefficients
N. Saradha, Divyum Sharma

TL;DR
This paper provides explicit upper bounds for the number of solutions to Thue inequalities involving forms with few non-zero coefficients, improving upon previous bounds by making all constants explicit.
Contribution
The paper introduces three explicit upper bounds for solutions of Thue inequalities with few coefficients, making all constants fully explicit.
Findings
Derived three explicit upper bounds for solutions
Improved upon previous bounds by removing undetermined constants
Applicable to forms with few non-zero coefficients
Abstract
Let be an irreducible form of degree and having non-zero coefficients. Let be an integer and consider the Thue inequality 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 where is an explicit function of and 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.
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Harmonic Analysis Research
