The field of Diophantine Equations has a long and rich history. It received an impetus with the advent of Baker’s theory of linear forms in logarithms, in the 1960’s. Professor T.N. Shorey’s contributions to Diophantine equations based on Baker’s theory is widely acclaimed. An international conference was held in his honour at the Tata Institute of Fundamental Research, Mumbai during December 16–20, 2005. This volume has evolved out of the conference and it reflects various aspects of exponential Diophantine equations.

Highlights in the Research Work of T.N. Shorey / An Extremal Problem in Lattice Point Combinatorics / Existence of Polyadic Codes in terms of Diophantine Equations / Some Problems of Analytic Number Theory — V / Powers From Five Terms in Arithmetic Progression / Linear Forms in the Logarithms of Algebraic Numbers Close to 1 and Applications to Diophantine Equations / T.N. Shorey’s Influence in the Theory of Irreducible Polynomials / Polynomial Powers and a Common Generalization of Binomial Thue-Mahler Equations and S-unit Equations / On the Diophantine Equation / On Numbers of the Form ±x2 ± y! / Linear Forms in Two and Three Logarithms and Interpolation Determinants / On a Conjecture of Shorey / Algebraic Independence in the p-adic Domain / Remark on p-adic Algebraic Independence Theory / Generalized Lebesgue-Ramanujan-Nagell Equations / Around Pólya’s Theorem on the Set of Prime Divisors of a Linear Recurrence / The Number of Solutions of Some Diophantine Equations / Logarithmic Functions and Formal Groups of Elliptic Curves / On the Greatest Square-Free Factor of Terms of a Linear Recurrence Sequence / Diophantine Approximation and Transcendence in Finite Characteristic / On Irrationality and Transcendency of Infinite Sums of Rational Numbers / The Role of Complex Conjugation in Transcendental Number Theory.

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