Formes linéaires de logarithmes et équations Diophantiennes

Résumé

The field of transcendance has a variety of subfields including : the transcendence of individual numbers, algebraic independence, transcendence of functions ( for example, modular forms, the zeta and $j$ functions, etc. ) at particular values, and applications to Diophantine equations which involve the linearly recurrent sequences (for example, Fibonacci numbers, Lucas numbers, Tribonacci numbers, Padovan numbers, and the Pell-Lucas numbers). In this work we have considered the number field in general, followed by the Diophantine equations, where we have explored some exponential Diophantine equations in linearly recurrent sequences. The method used to solve these equations is a double application of Baker's method and some computations with continued fractions to reduce the brute force search range for the variables. They combine elementary arguments with bounds for linear forms in logarithms and reduction techniques from the Diophantine approximation. We have also shown the application of the mathematical method of Diophantine equations in physics and chemistry.

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