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Diophantine Equations
Edited by: N. Saradha, Tata Institute of Fundamental Research, Mumbai, India
A publication of the Tata Institute of Fundamental Research.
Tata Institute of Fundamental Research
2007; 300 pp; hardcover
ISBN-10: 81-7319-898-5
ISBN-13: 978-81-7319-898-4
List Price: US$30
Member Price: US$24
Order Code: TIFR/12
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The study of Diophantine equations has a long and rich history, getting its impetus with the advent of Baker's theory of linear forms in logarithms, in the 1960's. T. N. Shorey's contribution to Diophantine equations, based on Baker's theory, is widely acclaimed. An international conference was held at the Tata Institute of Fundamental Research, Mumbai from December 16-20 2005, in his honor. This volume has evolved out of the papers contributed by several participants and non-participants of the conference. These articles reflect the various aspects of exponential Diophantine equations from experts in the field.

Narosa Publishing House for the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka.

Readership

Graduate students and research mathematicians interested in number theory.

Table of Contents

  • S. D. Adhikari, S. Baier, and P. Rath -- An extremal problem in lattice point combinatorics
  • G. K. Bakshi, M. Raka, and A. Sharma -- Existence of polyadic codes in terms of Diophantine equations
  • R. Balasubramanian and K. Ramachandra -- Some problems of analytic number theory--V
  • M. A. Bennett -- Powers from five terms in arithmetic progression
  • Y. Bugeaud -- Linear forms in the logarithms of algebraic numbers close to 1 and applications to Diophantine equations
  • S. David and N. Hirata-Kohno -- Logarithmic functions and formal groups of elliptic curves
  • M. Filaseta, C. Finch, and J. R. Leidy -- T. N. Shorey's influence in the theory of irreducible polynomials
  • K. Györy and A. Pinter -- Polynomial powers and a common generalization of binomial Thue-Mahler equations and \(S\)-unit equations
  • M. Kulkarni and B. Sury -- On the Diophantine Equation \(1+x+\frac{x^2}{2!}+\cdots+ \frac{x^n}{n!} = g(y)\)
  • F. Luca and A. Togbé -- On numbers of the form \(\pm x^2\pm y!\)
  • M. Mignotte -- Linear forms in two and three logarithms and interpolation determinants
  • Y. V. Nesterenko -- Algebraic independence in the \(p\)-adic domain
  • P. Philippon -- Remark on \(p\)-adic algebraic independence theory
  • M. R. Murty and V. K. Murty -- On a conjecture of Shorey
  • N. Saradha and A. Srinivasan -- Generalized Lebesgue-Ramanujan-Nagell equations
  • A. Schinzel -- Around Pólya's theorem on the set of prime divisors of a linear recurrence
  • W. M. Schmidt -- The number of solutions of some Diophantine equations
  • C. L. Stewart -- On the greatest square free factor of terms of a linear recurrence sequence
  • D. S. Thakur -- Diophantine approximation and transcendence in finite characteristic
  • R. J. Tijdeman -- On irrationality and transcendency of infinite sums of rational numbers
  • M. Waldschmidt -- The role of complex conjugation in transcendental number theory
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